Limits at Infinity, the number 1 is bigger than you may think

Originally posted by metamagic

[snip] It's a basic exercise for first year students to show that... [snip]

My sentiments exactly. There are quite a few things OP said that dont quite make sense, but your doing a much better job speaking math lingo than I could right now. It sounds to be like OP is a student who is preparing for Calc 101 finals. By the way OP, thanks for the refresher course! Now onto my nit-picking

When you say one infinity is larger than another, that doesnt quite make sense. Infinity is the same no matter what you do to it mathmatically. To say that an infinite number of points makes up an area of N, and also makes up an area of 2N means that one infinity is larger than the other is weird too. Its the same infinite number of points and this works because a point has 0 dimensions.

Further to say that I walk on a path forever, and someone else runs along my path forever, and that one of us went further is wrong as well. We both traveled the same infinite distance, its just that one of us is further along than the other. Same with the counting and exploding cookies. The computer counted to higher numbers than I counted FASTER, but that doesnt mean the computers infinity is higher. Same with cutting and exploding cookies. If you use explosives you may get more little pieces of cookie faster than I get them by cutting, but we both still end up with the same infinite amount of cookie pieces. (I also want to say that infinity is more than one can physically do, so using examples of physical actions doesnt quite make sense either, but Ill play along use your metaphors to show you where I think you went wrong.)

reply to post by PhysicsAdept

Because there can never exist perfection in nature that accurately resembles itself as being EXACTLY 1, when we use the number 1 we are referring to the approximation, or generalization of its value.

I am not sure if i agree. At one point in time the apple must reach "its own (1)" perfection/peak or maximum.

If monitored it can be displayed graphically.

Originally posted by PhysicsAdept
reply to post by metamagic

 

2. The stuff about z-scores and variance measures is gibberish. A z score is used to transform an arbitrary NORMAL distribution to a standard normal distribution mean mean=1 and s.d. = 1.

No, the z-score allows you to compare how something relates to something else, the weight of an apple compared to other weights below a normal curve vs. the the diameter of an apple compared to other diameters below a normal curve.

Perhaps a little example and analogy will help explain why you are struggling with the concept of a z-score. First a little analogy. Trigonometry is the tool we use for working with circles. There are two basic assertions that trigonometry makes: (1) The results are valid for all circles even though they are expressed in terms of unit circle, and (2) the results are valid ONLY for circles and not for ellipses, rectangles or other geometrical forms.

So if I have a circle centered at (1,1) and radius 4 and I want to know the co-ordinates of the point on the circle that is 30 degrees counter clockwise from the x axis. I could calculate this directly but that's really a lot of work. So I shrink the circle down to a radius of 1 and move it to left and down 1 so that it is a unit circle. Then I can use a trig table to figure out the point I want is at (cos 30, sin 30) which is (.866025404,.5) Now to get back to the original circle I multiply the result by 4 to get ( 1.732,2) and of course we have to move it back to its original position by adding (1,1) so the co-ordinates of the point I originally wanted are (2.732,3). But this only works if I start with a circle -- I can not use this technique if I started with square.

So a z-score is like a trig table. Lets suppose I start with a normal distribution with a mean=100 and a standard deviation of 10. and I want to know what value in the distribution are less that 105. Again, i could calculate the value directly by computing the area under the curve to the left of 105, but that is way too hard. So I convert this distribution into a "standard normal distribution" with mean=0 and sd=1. (I typo-ed in a previous post when I said the mean for a this distribution was 1. Oops.) So I convert this value to an equivalent value on the s.n.d. by subtracting the mean and dividing by the s.d which is (105-100)/10 = 5/10 = .5. This value .5 is called the z-score and is used to look up on a table the area under the curve for the which is 69.1463%. So I can say that 69% of the scores in our original distribution are less than 105. And of course we can also figure out what value 80% of the scores are greater than by using the z-score for 80% and then multiplying that by the s.d. and adding the mean.

Originally posted by PhysicsAdept
reply to post by metamagic

 

No reference to Euler's formula at all.

Bull! The only reason why you can call e and pi real numbers are because of his formula, e^(pi*i)+1=0 !

Euler's formula has (1) has nothing to do with the definition of pi or e, and (2) is a total red herring because it is a relationship between complex numbers not real numbers.

So then what are the definitions of pi and e? First of all the real numbers can be defined as the closure of the set of rational numbers. What that means is that when we have a Cauchy sequence of rational numbers (that is a sequence like [1/n] where the terms get arbitrarily close the further you go. Now the sequence [1/n] converges to [0] which is a rational number which is nice, but there are many sequences that don't. The set of all limits of all the Cauchy sequences of rational numbers is the closure of the rational numbers. So that means that e and pi can be defined as the limits of specific sequences of rational numbers. So here comes the fun part.

We can define e as the limit of (1 + 1/n) to the nth power as n approaches infinity.

Pi can be defined in terms of a simple continued fraction which is a number that looks like this



or in it's abbreviated notation.




So pi is defined as s.c.f to what is called the third convergent as



So that should pretty much eliminate the argument that the only reason e and pi are real is because of Euler's formula.

Which is pretty much a total misunderstanding of what a limit and number are. My suggestion is that if you want to publicly use mathematical terms and concepts, take the time to learn what they are. It's actually very interesting.

disprove it, go ahead. How is a number not a limit in and of itself? Because there can never exist perfection in nature that accurately resembles itself as being EXACTLY 1, when we use the number 1 we are referring to the approximation, or generalization of its value. In all likelihood, 1 in nature would really compute to a value of 1.000000000000000000000000000001 in whatever we were determining... You guys really are not getting this post. Confusedly too, seeing as you are obviously very intelligent.

No one said that number is not a limit, obviously every number x is the limit of the constant sequence [x,x,x,x,x...] But the question in mathematics is whether or not if we have a set of numbers N, the limits of the sequences of elements of N are also elements of N. For the rational numbers, the answer is no, for the real numbers the answer is yes.

Now everything after the question mark above has nothing to do with math, but is an expression of your personal beliefs about the nature of reality and how we use math to describe nature. I've only questioned the mistakes you have made in your description of math and statistics. The rest of it is a matter of your personal ontology.

reply to post by ChemistryAdept

I would like to begin by saying that you have contradicted yourself here. you are saying that you see 1 apple because you have grown up with the CONCEPT of it being one apple but he is wrong because his CONCEPT of one apple is not exactly 1 because his math (statistics) , which is what he grew up with, tells him otherwise.

Everyone sees one apple. He is a classic example of overthinking himself into confusing himself.

I can have 2 apples...a small ripe red apple and a large unripe green apple...and I still have two apples. The unit of "apple" is defined by society...not by math. But still...if he wants to create his own unit of the "perfect apple" based on taking measurements and calculating the ideal size, weight, color, etc....that is fine. And then he can go through all the apples and find some "perfect apples". Those "perfect apples" will be a subset of the larger set of "apples".

But you can't take an apple and say "you don't have 1 apple there...you have half of a perfect apple because it's color isn't quite right". It just doesn't make sense. You can say, "That apple you have have is 50% perfect based on my criteria of a perfect apple." But the only way to have half of a perfect apple is to first find a complete perfect apple and cut it in half.

You are saying that concepts are bad because your concept disagrees with it, correct?

I am in no way saying concepts are bad.

What is bad is trying to use a concept as a number.

And you are saying you can find all of these things in concept, such as the area of a circle, but he is not allowed to find infinity as a number IN CONCEPT? If you are going to constantly tell someone they are wrong, and you give an example of their 'error', do not use the same error in your next post

You seem to be just as confused as him. Concepts are great to use when used correctly.

In real life you can't find the exact area of square...because any measurment you take is not exact. The units of measure we use can be broken down infinitely. For example...we can measure the dimensions of a square in meters, that will give us an approximation...probably not a good one if it is a small square. But if we use centimeters...we get a better estimate. We use milimeters, even better. We can continue to break down that unit of measure forever infinite amount of times and continue to get to a better estimate...but you can never find the exact area.

Now in CONCEPT, it is easy. If we CONCEPTUALIZE a perfect and exact 1 inch by 1 inch square...we know the area is exactly 1 square inch. That is using a concept in the correct way.

In real life and concept we can never know the exact area of a circle because pi is an irrational number. In an earlier post I said you could, but you can't because of pi beign irrational (sorry, it was late).

But you can NOT use the concept of infinity as a number...you just can't do it because it is NOT a number. It would be like using "large" as a number and saying 1/large is zero because the limit approaches zero. He is continuing to try to replace 1/n as n approaches infinity as zero...and he is just flat out wrong. It is NEVER zero...it continually approaches zero but never ever gets there. He is also trying to use mathematical operations on infinity...which you can't do...you can't divide infinity by anything, you can't multiple it by anything, you can't add anything to it...because it is a CONCEPT...not a NUMBER.

He is using that basic flaw as the basis for his entire premise.



It's nice of you to come back up your friend, but you seem to be as confused about this topic as he is.

reply to post by PhysicsAdept

It's a bit funny ain't it? He sits there and tells me that no one cares about the perfect apple and that we just group all apples into what tree they came from and then he goes on to tell me that a unit (here the unit is apple) is not a generalization itself.

What I'm telling you is that you are using a different unit than everyone else is....and even with that...you are using it wrong.

Everyone else says "Hey...I have 1 apple" based on the definition of apple society has agreed upon. You come along and say "No...you have 0.75 of an apple based on me calculating what a "perfect apple" is...and your apple only conforms to 75% of the criteria."

Two problems...first, you are using a unit of a "perfect apple" while everyone else is using the unit of "apple". Second, you aren't even using your unit correctly. The only way I could have 75% of a "perfect apple" is if I started with one whole perfect apple, cut it up into pieces and kept 75% of them. Can a car be said to be some fraction of a train because they both have wheels? Could I say, oh...I don't have 1 car...I have 7% of a train???

You are mind effing yourself and have confused yourself into thinking you have stumbled onto something brilliant.

1/infinity (limit- wise) approaches zero. Now, we keep talking about infinity. Some people here would argue that I speak of it as a number, I will not disagree with that here (though I merely believe it should be looked at as a plane, not a number itself.) but, you cannot refer to an infinity as a concept and then argue that 1/infinity does not equal zero. Because in concept, it very realistically will

1/infinity is UNDEFINED.

You can not perform mathematical functions on the CONCEPT of infinity. You can take the limit of a function as it approaches infinity...and the answer to the limit of 1/n as it approaches infinity is zero...becuase the LIMIT is zero. The answer to 1/infinity IS NOT ZERO.

I don't know how else to say this...you obviously don't understand it. A LIMIT is not an EQUALITY...if you don't comprehend this...you will never understand why you are wrong.

Let me write it again so maybe you understand.

THE LIMIT of 1/n as n approaches infinit is ZERO....THE LIMIT IS ZERO.

1/infinity IS NOT DEFINED.

Am I truly overthinking this? I thought I brought common sense into discussion. Thinking is a byproduct of discovery, perhaps some people on this thread have not yet discovered their own minds enough

You are completely overthinking while using incorrect logic to bring yourself to a very very wrong conclusion.

I can tell you think you have found something brilliant...but it is only because you don't fully understand the concepts you are working with.

Originally posted by OutKast Searcher
reply to post by ChemistryAdept

 

I would like to begin by saying that you have contradicted yourself here. you are saying that you see 1 apple because you have grown up with the CONCEPT of it being one apple but he is wrong because his CONCEPT of one apple is not exactly 1 because his math (statistics) , which is what he grew up with, tells him otherwise.

Everyone sees one apple. He is a classic example of overthinking himself into confusing himself.

I can have 2 apples...a small ripe red apple and a large unripe green apple...and I still have two apples. The unit of "apple" is defined by society...not by math. But still...if he wants to create his own unit of the "perfect apple" based on taking measurements and calculating the ideal size, weight, color, etc....that is fine. And then he can go through all the apples and find some "perfect apples". Those "perfect apples" will be a subset of the larger set of "apples".

But you can't take an apple and say "you don't have 1 apple there...you have half of a perfect apple because it's color isn't quite right". It just doesn't make sense. You can say, "That apple you have have is 50% perfect based on my criteria of a perfect apple." But the only way to have half of a perfect apple is to first find a complete perfect apple and cut it in half.

An excellent and insightful analysis, especially the part about "apple" being defined by society not by math. For example, where I live "Film" like in camera film is a mass noun. You can have film, lots of films, some film -- sort of like water. However in the West Indies, film is a count noun where it is natural to say "pick me up a couple of films for my camera at the store".

This whole approach again is the work of a lot of scientific inquiry, esp in cognitive psychology and the work of Dr. Eleanor Rosch. A little edited snippet from Wikipedia which should be a great starting place for anyone interesting in this totally fascinating approach

Eleanor Roschis a professor of psychology at the University of California, Berkeley, specializing in cognitive psychology and primarily known for her work on categorization, in particular her prototype theory, which has profoundly influenced the field of cognitive psychology. Throughout her work Rosch has conducted extensive research focusing on topics including semantic categorization, mental representation of concepts and linguistics.. Her research interests include cognition, concepts, causality, thinking, memory, and cross-cultural, Eastern, and religious psychology.

From field experiments she conducted in the 1970s with the Dani people of Papua New Guinea, Rosch concluded that when categorizing an everyday object or experience, people rely less on abstract definitions of categories than on a comparison of the given object or experience with what they deem to be the object or experience best representing a category. Although the Dani lack words for all the English colors (their language contained only two color terms dividing all colors into either the 'light, bright' category or the 'dark, cool' category), Rosch showed that they could still categorize objects by colors for which they had no words. She argued that basic objects have a psychological import that transcends cultural differences and shapes how such objects are mentally represented. She concluded that people in different cultures tend to categorize objects by using prototypes, although the prototypes of particular categories may vary.

en.wikipedia.org...

The whole topic of infinities and how they work can be both fascinating and intimidating since once we start to get into the more rarefied areas of set theory we start to deal with counter-intuitive results. Such as this gem called the axiom of choice.

Informally put, the axiom of choice says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin. In many cases such a selection can be made without invoking the axiom of choice; this is in particular the case if the number of bins is finite, or if a selection rule is available: a distinguishing property that happens to hold for exactly one object in each bin. For example for any (even infinite) collection of pairs of shoes, one can pick out the left shoe from each pair to obtain an appropriate selection, but for an infinite collection of pairs of socks (assumed to have no distinguishing features), such a selection can be obtained only by invoking the axiom of choice.

en.wikipedia.org...

However there is a brilliant book by Rudy Rucker called "White Light" which is a sort of an Alice in Wonderland adventure of a mathematician who travels to a different reality where the various infinities are just ordinary numbers, that you can count with; so you can count, for example, up to infinity. In the tradition of "Flatland" I recommend it to anyone who loves to think about infinities.

Amazon.com's review

Malcontent mathematics instructor Feliz Raymond's afternoon naps are the subject of Rudy Rucker's strange and delightful White Light. Bored with his life and job at a state university in New York and making no headway in solving Georg Cantor's Continuum Problem, Raymond finds himself every afternoon, lying flat on his floor, entering into a state of lucid dreaming that allows him to explore an entirely new surreal and mathematically-charged reality. What follows is an adventure through time and space, the likes of which only a collaboration between Umberto Eco and Lewis Carroll could attempt. With traveling companions ranging from Einstein to the devil to a giant beetle named Franx, Raymond explores the infinite reaches of his new playground, which is filled with a multitude of cultural and scientific references, some subtle and many overt. Each turned corner of White Light is another gleeful surprise, another celebration of cleverness and imagination. Rucker, who is just as comfortable presenting accessible introductions to modern ideas in geometry (The Fourth Dimension: A Guided Tour of the Higher Universes) as he is spinning yarns of hacker fiction (The Hacker and the Ants), wrote this novel while, like the protagonist, endeavoring to solve Cantor's Continuum Problem at a state university in New York.

reply to post by OutKast Searcher


Ok, look. There is nothing I can do to profess my point more clearly. I have tried all that I know. I still stand by that you and I are on the same page. Your metaphors are either further proving what I am saying or they are tangential. If you look at my original point, I was merely saying that there must exist some infinities out there, some undefined unquantifiable number that exists in a very small place. There is more to everything than what we consider. Beyond that, infinity, as a numerical description can be applied somewhat in relativity. Involving the whole walk and run example, understand that both you AND I know that both distances equal infinity. the time it gets to reach this plane of infinity, NOT AN ACTUAL NUMBER (I get this even though you would swear up and down I do not) is much reduced from rate to another, and thusly something like the ln(x) will be less infinite than 10^x. You would be amused on how much of what we are saying is the same...

For just one second, stop looking at the things you read in a book and just think, independently. Don't try to show your authority by quoting tid bits of what I say, just speak your mind. And then tell me, was anything I mentioned inconcievable? Infinity is not something, (first of all that can be proven in favor of you or I) that is just categorized similarly for every event. Can you not see a grain of truth to what I say? If I sat here and wanted to profess accepted math theory, then who would have listened? Anyone who cared in math you not need to see this. I am merely trying to explore other realms. You can attempt to shut me down, but where does that get any of us?

I want this to be a thought experiment, not a pissing match. Deny that this hasn't been one, and I am afraid that either I am the dumbest person alive and you are supreme king of the universe, or accept that maybe there is no way to disprove what I am saying, and therefore maybe we can discuss what it means--not that your book told you one thing that slightly differs from what I am saying.

I wanted a friendly exploration of infinity, and look. It has caused arguments that are getting nowhere. Where is the learning? I seek knowledge through discussion, not stagnation. If you do not wish to attempt in that endeavor, I am afraid I will not reply anymore.

This is why politics does not work, this is why the world sucks. No one wishes to listen. In no way am I asking for everyone and bow down to my ideals either, I just want to be helped and guided, as do I wish to help and to guide.

Math, beyond the physical numbers, is all speculation. To deny the concept of infinity as something that has a flexible meaning, would be to end the entire point of why the term infinity ever even came to existence. Infinity, is it not there to represent those numbers we cannot count? We look to infinity to describe a concept of something that no one has yet actually encountered--which is everything.

I know I am not the best person in communicating my thoughts, but I was hoping someone like you would be able to read between the lines and figure out the true meaning of my intent...

I suppose I have no paper describing my 8 years of collegiate mathematics, yet that does not mean I deserve to be completely discounted in having an idea. Remember, none of what I said can really be proven or disproved, so why cannot we focus on getting it to that point?

Again, I ramble. People like you make people like me wish that websites like this never existed. No such thing as a think-tank. It is a myth apparently.

Originally posted by PhysicsAdept
People like you make people like me wish that websites like this never existed. No such thing as a think-tank. It is a myth apparently.

Harsh.. However, it is a bit of a myth. Perhaps as social interactions evolve through technology, we will start to see more of it seeping in. Though, they still may not be accessible to all. C'est la vie

Once we "adapt" 1 to include the space from 0 to infinity, we can apply it to many things through iterations. I figure you already know this OP, but maybe another viewpoint on the same thing will be useful. The space in between the integers is a very interesting space for it "all" to happen.

Math is used for us humans to better understand the world around us. It is in patterns and constant motion. We can apply these mathematics strictly as derivatives, and when we find a pattern exhibiting, we explore it. Smells like science However, the point you bring up greatly illustrates the weaknesses in our understanding of the patterns manifestations (as apples). The apples themselves are "perfect" in the way that they formed exactly as they would given those specific variables and environment. They may not illustrate the "perfect" apple as illustrated by human derived averages, but if the variables change, so does the product. Its completely predictable, in that sense. Amazing the scale that this is happening on...

The "1" can be used as an interesting term in so many ways. Quite versatile! However, when we speak of infinity in philosophical terms (perhaps more meaningful than human-based patterns that inherently can not contain it), it is essentially an "all-consuming" item to my eyes. For my thought processes, it evolves from something that is everything (infinite) to including even myself. It is that very thought experiment that started my explorations into "experiencing the math" for myself.

I appreciate that you have given so many of your thoughts. The response was strange, really.

reply to post by OutKast Searcher


Layman's Terms it is....
Y=.0001X
Y=X^X
put this in your pretty little calculator and graph it.
which one grows faster? X^X. therefore it shall in concept reach infinity faster. By the time .0001X reaches this infinity then X^X is even BIGGER! Therefore it is at a bigger infinity!!! who would have thought that one infinity could be bigger!

PS. about the apples, if you can generalize that an apple that fits 50% of the criteria is an apple, then why aren't you generalizing that an infinity small number is zero?

Just read through the whole thread here, and I believe I understand the gist of what OP is saying and here is my OPINION on the whole thing.

I believe that we live in an infinite universe. This paradox I believe is attributed to man trying to "contain" infinity. Basically, I'm saying that math is a wonderful tool, but it can never be 100.00% accurate.

Originally posted by metamagic

Originally posted by PhysicsAdept
reply to post by metamagic

 

No reference to Euler's formula at all.

Bull! The only reason why you can call e and pi real numbers are because of his formula, e^(pi*i)+1=0 !

Euler's formula has (1) has nothing to do with the definition of pi or e, and (2) is a total red herring because it is a relationship between complex numbers not real numbers.

So then what are the definitions of pi and e? First of all the real numbers can be defined as the closure of the set of rational numbers. What that means is that when we have a Cauchy sequence of rational numbers (that is a sequence like [1/n] where the terms get arbitrarily close the further you go. Now the sequence [1/n] converges to [0] which is a rational number which is nice, but there are many sequences that don't. The set of all limits of all the Cauchy sequences of rational numbers is the closure of the rational numbers. So that means that e and pi can be defined as the limits of specific sequences of rational numbers. So here comes the fun part.

We can define e as the limit of (1 + 1/n) to the nth power as n approaches infinity.

Pi can be defined in terms of a simple continued fraction which is a number that looks like this



or in it's abbreviated notation.




So pi is defined as s.c.f to what is called the third convergent as



So that should pretty much eliminate the argument that the only reason e and pi are real is because of Euler's formula.

Which is pretty much a total misunderstanding of what a limit and number are. My suggestion is that if you want to publicly use mathematical terms and concepts, take the time to learn what they are. It's actually very interesting.

disprove it, go ahead. How is a number not a limit in and of itself? Because there can never exist perfection in nature that accurately resembles itself as being EXACTLY 1, when we use the number 1 we are referring to the approximation, or generalization of its value. In all likelihood, 1 in nature would really compute to a value of 1.000000000000000000000000000001 in whatever we were determining... You guys really are not getting this post. Confusedly too, seeing as you are obviously very intelligent.

No one said that number is not a limit, obviously every number x is the limit of the constant sequence [x,x,x,x,x...] But the question in mathematics is whether or not if we have a set of numbers N, the limits of the sequences of elements of N are also elements of N. For the rational numbers, the answer is no, for the real numbers the answer is yes.

Now everything after the question mark above has nothing to do with math, but is an expression of your personal beliefs about the nature of reality and how we use math to describe nature. I've only questioned the mistakes you have made in your description of math and statistics. The rest of it is a matter of your personal ontology.

Here think about this why should we be limited to finding pi only one way
-It take 3 point to triangulate something
-Averages can be found in three ways--mean, median and mode.


Pi (3.14159265...) can only be rational if you make 2 circles one inside the other put 2 on both sides of the inside one which is truthfully the same as the outer circle their both 0s right

The inside one just has a circle +1 and a -1 or -1, +1 or circle ( A ) and ( B ) the center one we will call ( O ) and the outer ( o ) So ( O ) = (o) but ( A ) and ( B ) do not equal ( o )
but each one A or B does equal ( O ) the center circle But ( A ) and ( B ) are polarities to the other

You see Infinity is both within and without the ( O ) center circle and ( o ) outer circle making them 2 the same But one different the ones ( A ) and ( B ) are only different from ether ones + or - perspective if you use all the 3 inside circles radius ( A ) ( O ) ( B ) and across the big circle ( o ) and rap the central ( O ) with that you get 9.1428571428571428571428571428571... much more rational

This is a fascinating thread. S&F

When engineers developed early jet planes, they came across a major problem when designing control surfaces on the wings. As the jet approached supersonic speed, the force required to operate the control surfaces approaches infinity. To combat this problem, engineers had to redesign the whole wing & control surfaces to compensate.

I can see where the OP is coming from.

As to the human analogy with skin cells. I think that this is a scenario that appears to be infinite, but can be quantified in whole numbers. IMHO anyway.

Originally posted by ChemistryAdept

Layman's Terms it is....
Y=.0001X
Y=X^X
put this in your pretty little calculator and graph it.
which one grows faster? X^X. therefore it shall in concept reach infinity faster. By the time .0001X reaches this infinity then X^X is even BIGGER! Therefore it is at a bigger infinity!!! who would have thought that one infinity could be bigger!

There is a fundamental flaw in your logic here. One cannot 'Reach' Infinity. Infinity is boundless and has no end.

A bit like chasing the pot of gold at the end of the rainbow, you'll never get there, and the faster you move - the faster the pot moves

reply to post by PhysicsAdept


I love thought experiments and letting your mind explore the unknown...but you have to do it with logic and rationality.

But if you break the definition of a concept...we are no longer just academically exploring new ideas...we are going into pure fiction.

There are things you have started out with that are incorrect and will lead you and others reading this thread into a complete false sense of understanding of mathematical concepts. Sorry...but I'm going to point out those errors when I see them so other people don't read this thread, pick up false information, and become more ignorant due to it.

If we want to just explore fantasy with no regard to reality...that is fine...but let's not pass it off as real mathematics.

And yes...I do have to disagree with you when I see things that are just wrong.

Beyond that, infinity, as a numerical description can be applied somewhat in relativity. Involving the whole walk and run example, understand that both you AND I know that both distances equal infinity. the time it gets to reach this plane of infinity, NOT AN ACTUAL NUMBER (I get this even though you would swear up and down I do not) is much reduced from rate to another

You can not reach infinity...this is where you and your friend go wrong.

It doesn't matter if you walk or run...you never reach infinity. At any given time, the person running will have traveled a greater distance than the person walking has...but they will never reach infinity. They could walk/run for an infinite amount of time and they still won't reach infinity. At any given time, they have both traveled a FINITE distance...they can never travel an INFINITE distance.

I wanted a friendly exploration of infinity, and look. It has caused arguments that are getting nowhere. Where is the learning? I seek knowledge through discussion, not stagnation. If you do not wish to attempt in that endeavor, I am afraid I will not reply anymore.

And many people have tried to teach you that your understanding of infinity is off...you just don't want to accept that knowledge.

The only knowledge you are seeking is that your idea is right...and no one can give that to you because you are just flat out wrong.

Infinity, is it not there to represent those numbers we cannot count? We look to infinity to describe a concept of something that no one has yet actually encountered--which is everything.

Infinity is simply a way to describe an unbound set. The error you are making is that you are using a description of a boundry as a number.

Like I said before...it is just the same as trying to use "large" as a number.

People like you make people like me wish that websites like this never existed. No such thing as a think-tank. It is a myth apparently.

Why? Because I questioned you and dared to point out the errors in your logic?

If you were truly seeking knowledge...you would welcome people point out the flaws in your logic and reasoning.

I too enjoy brainstorming and trying to think outside the typical thought. You actually may enjoy my very first thread on ATS.

www.abovetopsecret.com...

And I wish I could re-create that thread because I know I didn't do a great job of explaining my thoughts in that thread.

Originally posted by ChemistryAdept
reply to post by OutKast Searcher

 

Layman's Terms it is....
Y=.0001X
Y=X^X
put this in your pretty little calculator and graph it.
which one grows faster? X^X. therefore it shall in concept reach infinity faster. By the time .0001X reaches this infinity then X^X is even BIGGER! Therefore it is at a bigger infinity!!! who would have thought that one infinity could be bigger!

PS. about the apples, if you can generalize that an apple that fits 50% of the criteria is an apple, then why aren't you generalizing that an infinity small number is zero?

edit on 18-3-2012 by ChemistryAdept because: Damn Typos...

A function will never reach infinity...therefore there is no "bigger infinity".

At any finite value for X there is a finite value of Y...and for any given finite value of X, Y1 will be smaller than Y2.

They NEVER reach infinity.

Both of you seem to have a fundamentally flawed understanding of infinity.


Where did I say that "an apple that fits 50% of the criteria is an apple"??? I am pretty sure I said exactly the opposite of that. If it only meets 50% of the criteria...then it is not an apple. And an infinitely small number is NOT zero...it is just very small (I would say infinitely small...but you clearly mis-understand that word).

reply to post by Riakennor, post by IntegratedInstigator,post by sinohptik,post by graphuto,post by OccamAssassin,post by metamagic,post by OutKast Searcher,post by Americanist,post by IblisLucifer,post by ChemistryAdept,post by selfharmonise,post by AlienAnthropologist, and post by spy66

Ok I feel like this thread needs to be reexamined. I am going to post a new thread where I invite each of you that have participated in this thread to join. I would love it very much to discuss this topic further, but I am going to try to organize things better so that we can focus more on what I wan to, which is concept. Thanks!

P.S. I really would like all of your input, but in the new thread. Even if things must be repeated, I personally feel it is necessary. Then of course, we should continue discussion here as well, when necessary.

Math Philosophy-- Why does 1/∞ not equal 0, and for that matter, what is ∞?

The Number 1 is the accumulation of All, the Infinite.

If = 1

Each and every One of us is a finite piece of that One, as an individual One of WE the finites.

Ribbit

Originally posted by Riakennor

Originally posted by ChemistryAdept

Layman's Terms it is....
Y=.0001X
Y=X^X
put this in your pretty little calculator and graph it.
which one grows faster? X^X. therefore it shall in concept reach infinity faster. By the time .0001X reaches this infinity then X^X is even BIGGER! Therefore it is at a bigger infinity!!! who would have thought that one infinity could be bigger!

There is a fundamental flaw in your logic here. One cannot 'Reach' Infinity. Infinity is boundless and has no end.

A bit like chasing the pot of gold at the end of the rainbow, you'll never get there, and the faster you move - the faster the pot moves

Reality exists between 2 points of infinity