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

Someone may have mentioned this but look at Cantor's proof that the cardinality of the set of rational numbers corresponds to the cardinality of the integers. It is a fascinating proof.

Also, find his "diagonalization" proof that the cardinality of the real numbers is greater than the cardinality of the rationals. From this we get the idea of "levels" of infinity.

I believe in the Continuum Hypothesis, by the way, even though it is formally undecidable according to the laws of Set Theory as yet described.

Best of luck in your education to the OP.

Originally posted by Qumulys
reply to post by djeminy

 

DAWG is basically slang for dog, started as a meme like this.

but this thread needs one more along these lines.

Got it - thanks mate!

Love your graphic illustrations, very cleverly done .....

Cheers

Originally posted by djeminy

Originally posted by longjohnbritches
reply to post by djeminy

 

I hear ya dj ,
Where there is a will there is a way with feminity. an infinite one
You DAWG you, thanks for the reply

Hi ljb,

my inexhaustible boundless curiosity demands to know what
DAWG stand for?

We 'Vikings' still have a lot to learn from the languages of other
tribes!

Many thanks in return -

Cheers

Hi dj

Looks like you already received an answer.
By the way have you seen the Hatchet job post on Vikings in Lost Civilizations?
I thought your anology of infinity, as being sexual in nature, was true.
Because with out procreation thought vanishes. And without thought there is O.
the best
ljb
Actually after seeing the graphics I'll give you my answer.
You would have to go to some old American Idol show and see and hear Randy describe Steven Tyler. Not excatly my tribe

reply to post by PhysicsAdept


Hi phys

I was wondering if you have learned anything so far.
You said in your opening that you knew nothing.
I see you have many flags, congradulations.
Not to shabby for comming here seeking advice and collaboration.
Speaks well about your desire to learn
the best ljb

Originally posted by PhysicsAdept
reply to post by MeesterB

 

So then at infinity, would it not equal 0?

I mean, at a very large number it would equal close to zero but we are not talking about a number at all. We are talking about a concept. So then conceptually, would not 1/∞=0?

I know you understand the concept of infinity, likely much better than I, and know much more about math than I could ever hope to know. Pre-calc was the highest I took and I barely use any of that... ever. I don't know if it's been mentioned or not (I didn't read everyone's post) but here is the main issue that I'm seeing.

"At infinity"

You can never actually be "at infinity" and so there is no way to theorize what would happen at that point, because it's not really a point at all. Being a minister, I would most closely relate the term infinity with the length of eternity. So to speak of arriving "at infinity" is almost like asking "what happens at the end of eternity?"
There is no end, and so the premise of the question itself is flawed. At least, that's how I'm seeing it. Have fun thinking about it though!

Originally posted by Mykahel

Originally posted by PhysicsAdept
reply to post by MeesterB

 

So then at infinity, would it not equal 0?

I mean, at a very large number it would equal close to zero but we are not talking about a number at all. We are talking about a concept. So then conceptually, would not 1/∞=0?

I know you understand the concept of infinity, likely much better than I, and know much more about math than I could ever hope to know. Pre-calc was the highest I took and I barely use any of that... ever. I don't know if it's been mentioned or not (I didn't read everyone's post) but here is the main issue that I'm seeing.

"At infinity"

You can never actually be "at infinity" and so there is no way to theorize what would happen at that point, because it's not really a point at all. Being a minister, I would most closely relate the term infinity with the length of eternity. So to speak of arriving "at infinity" is almost like asking "what happens at the end of eternity?"
There is no end, and so the premise of the question itself is flawed. At least, that's how I'm seeing it. Have fun thinking about it though!

Hi mike,
Forgive me If I am butting in.
The op may be on spring break or something like that Or the op may be here in some time in infinity. The op said he /she was just starting to learn this stuff.
Well i'll take a stab at your question because I have found it an interesting thread. I also asked phys what phys has learned on this thread. No answer as yet.
So here goes and I think I know what you are hedgeing at BUT lets open that can of worms anyway Eternity implies a begining. Infinity don't got one.
In other words, eternal with no begining or end.
Don't know if that helps
the best ljb

Thought I'd try and tackle the "Why doesn't it equal zero?" part of the question. Since I am a foreigner to the language of math, I'll be using an illustration like all good preachers do :-P

1/∞ has value. It has existence. 0, however, represents non-existence.
1/∞ seems small because 1 is so little compared to ∞. Divisions are essentially comparisons between the value of one number to the value of another.

Now, an ant is a very small creature compared to a human. Humans are very small compared to skyscrapers. Skyscrapers are very small compared to the size of the Earth. The Earth is small compared to the galaxy, which is small compared to the universe, which in theory is always expanding.

Even though the universe may continue to expand infinitely, and so our size may be infinitely small in comparison, but yet here we are. The size of the universe as it continues to grow does nothing to change our value/size. It does not require that we cease to exist, turning 1 into 0.

In other words, the continued growth/increase of ∞ will never change the value of "1"

Originally posted by Mykahel
Thought I'd try and tackle the "Why doesn't it equal zero?" part of the question. Since I am a foreigner to the language of math, I'll be using an illustration like all good preachers do :-P

1/∞ has value. It has existence. 0, however, represents non-existence.
1/∞ seems small because 1 is so little compared to ∞. Divisions are essentially comparisons between the value of one number to the value of another.

Now, an ant is a very small creature compared to a human. Humans are very small compared to skyscrapers. Skyscrapers are very small compared to the size of the Earth. The Earth is small compared to the galaxy, which is small compared to the universe, which in theory is always expanding.

Even though the universe may continue to expand infinitely, and so our size may be infinitely small in comparison, but yet here we are. The size of the universe as it continues to grow does nothing to change our value/size. It does not require that we cease to exist, turning 1 into 0.

In other words, the continued growth/increase of ∞ will never change the value of "1"

Some thuth here. well alot actually.
You see to accept any # or concept takes faith.
You as a minister are hard pressed to follow the teachings.
Us heathens don't have to. But it takes faith in something in the circle of infinity to ( I don't know why it is represented 8) to stay on the merry-go- round.
Hense the #1 something/anything Christ's tomb, aunt Tillies toenail.

Earlier I referred to Peter Rowland's book "The Foundation of Physics -- zero to infinity" -- I've now found a pdf paper of his that summarizes his analysis of infinity in more accessible language -- here you go pdf Are there alternatives to our present theories of physical reality?
Peter Rowlands

Originally posted by longjohnbritches

Originally posted by djeminy

Originally posted by longjohnbritches
reply to post by djeminy

 

I hear ya dj ,
Where there is a will there is a way with feminity. an infinite one
You DAWG you, thanks for the reply

Hi ljb,

my inexhaustible boundless curiosity demands to know what
DAWG stand for?

We 'Vikings' still have a lot to learn from the languages of other
tribes!

Many thanks in return -

Cheers

Hi dj

Looks like you already received an answer.
By the way have you seen the Hatchet job post on Vikings in Lost Civilizations?
I thought your anology of infinity, as being sexual in nature, was true.
Because with out procreation thought vanishes. And without thought there is O.
the best
ljb
Actually after seeing the graphics I'll give you my answer.
You would have to go to some old American Idol show and see and hear Randy describe Steven Tyler. Not excatly my tribe

edit on 22-3-2012 by longjohnbritches because: (no reason given)

Hi ljb,

Nice reply, thanks again -

actually, haven't seen the 'hatchet job' you refer to, but would be very interested to read about it!

Would be good if you had a link handy you could show me - perhaps?

Thanks in advance ....

Cheers

What is 1 divided by the infininte?

Actually what you must have is: 1 divided by 1 infinite.

You can't have 1 divided by zero. Because, zero dosen't exist physically.

Question:

How do you physically divide something by Zero? That has never ever been done scientifically or in any other way. except on a calculator.

Question 2:

How would you divide 1 by 1 infinite?

It can't be done.

If you have 1 gold nugget. How would the infinite divide it? What mathematical law do we have that can prove the cause?

The infinite would never divide the gold nugget.

If you only had 1 and 1 infinite. What would happen?