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Vivisekt wrote:What you're thinking of is the philosophical concept of an infinite number - which, really, isn't math. Calculus doesn't work that way.
Another one which is fun (if you don't want to see 1=0.999...) is
I was just bored I guess.
The difference between .999... and 1 is infinitesimal, but not non-existant.
0.999... is an expression of 1. Mathematics has certain definitions and 0.999... and 1 are the same thing. No number can possibly exist between them.
This doesn't make sense to me; just because "mathematics" defines something does not mean it is true. You say that no number can possibly exist between them. Then you are assuming that because the "distance" between the numbers is essentially 0, that they are the same number.
The difference that I have yet to see anyone say is that the difference between the two and the reason they aren't in reality equivlant, except by logical deduction, is that one is a finite number and .999... is an infinite number.
I have to disagree with this. What are we writing when we write 0.9999...? We are not writing an 'infinite number', but rather a number expressed as an infinite sum.
Day Zero wrote:This doesn't make sense to me; just because "mathematics" defines something does not mean it is true.
Kitty wrote:The difference that I have yet to see anyone say is that the difference between the two and the reason they aren't in reality equivlant, except by logical deduction, is that one is a finite number and .999... is an infinite number.
That's what I meant. Though it is a number expressed infinitely.
You can do .99999999999999999999999999999
99999999999999.... and never reach the end.
Potemkin wrote:You seem to be thinking of this almost as a temporal infinity; that you add each term after a couple of seconds. Obviously, in that case you never would get to the end. But it's not a temporal process. We can imagine adding each new term at the same time. There's no reason why we can't add all the terms at once.
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