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originally posted by: tridentblue
a reply to: AllIsOne
It makes for less trouble in the mind if you replace the word with "unlimited". The limit generally comes from somewhere else.
edit: If are a math guy who wants a way to look at this that fits your intuition that that the hammers should weigh more as I do, think of a 20 sided dice, with 10 red sides labelled 0-9 and 10 green sides labelled 0-9. To use it, you role it and write down the digit, and role again if it was green, or stop if you got a red digit.
How many outcomes can this dice produce using it that way? An infinite amount. The odds of a 100 digit number (get green sides 100 times in a row) are low, but possible. Even lower for 1000 or a billion digits, but still possible. Even though there are an infinite number of outcomes, there is still an *expected value*, which is the amount you would expect to get on average each round if you played this game and got the amount (in dollars) written down on the paper each time. Infinite sets in this way can have finite expected values. Multiplying that number times the "weight"/"payout" gives you a way to think of infinite sets in finite terms. Thinking this way is about seeing probability as fundamental.
originally posted by: AllIsOne
I seem to have a hard time with the abstract term "infinity". So here is my question. What is heavier: an infinite amount of feathers, or an infinite amount of hammers?
Mods: please move if in the wrong forum. I wasn't sure where to post.
originally posted by: AllIsOne
I seem to have a hard time with the abstract term "infinity". So here is my question. What is heavier: an infinite amount of feathers, or an infinite amount of hammers?
originally posted by: pheonix358
The answer is simple.
The question is invalid.
Infinity is not a number. It is a concept. You can not weigh a concept.
You cannot use infinity in any equation.
Zero has two functions. It is a place holder in our numbering system and it is the concept of nothingness. You cannot use it in equations either.
Infinity and zero are ideas, you can't really use them. So many people, some with years of study, just don't get it.
P
originally posted by: pheonix358
a reply to: AllIsOne
They are wrong.
You cannot use infinity in an equation. It is not a numerical value.
6 divided by zero is saying 'How many nothings are in 6' It is a stupid question.
I would even suggest you think about infinity over infinity. Most people will tell you the answer is 1.
But if you first look at 1 over infinity then the answer can be 0
Putting that into the first part then has infinity multiplied by nothing and that is nonsensical.
Most people can't get it at this level. They can only fall back on what they were taught by rote.
P
originally posted by: pheonix358
a reply to: AllIsOne
That is your choice. He is wrong
I don't give a flying kick who he is. Wrong is wrong.
P
originally posted by: Ceeker63
a reply to: AllIsOne Let me take a stab at this. Which is heavier a lb of hammers or a lb of feathers? It is a trick question of sorts. A lb of anything is still a lb. So comparing two object does not matter. They both weight a lb.
Infinite in your example = same
originally posted by: OrphanApology
a reply to: pheonix358
Actually you can use infinity in an equation to mark infinity. It's not a number but it's still there.
Like zero, it has it's place.
Also, just because something is an idea doesn't mean that it can't be explored and thought about.
Right now, to our knowledge it's impossible to accelerate an object faster than the speed of light(or even get anywhere near it) But that didn't stop Einstein from imagining it which helped him come up with his special relativity.
Imagination is important even when dealing with ideas that aren't realistic in any sense.
Obviously an infinite number of feathers is not based on a realistic situation, therefore it will always be an idea.
However if you add one to infinity it will always be infinity, therefore the feathers and the hammers would weigh the same in an infinite space even if they might weigh more or less than one another when in a place that is finite because the added weight would mean nothing.
Ohh my head hurts now.
Time for more coffee.