Why isn't infinity a number?
I haven't read any
proofs here about why it
actually isn't.
If the only reason it isn't is because it isn't defined, then wouldn't that suggest that the reason any number is a number is also simply the result of a definition? If that is so, wouldn't you satisfy mblase's statement, and you have: easily prove(n) that all numbers are equal to each other and mathematics as a discipline is a bunch of self-contradictory nonsense.
ie. if all numbers are purely defined concepts, then they are equatable simply as defined concepts.
Of course I am playing with language and reasoning but here is a more reasonable question:
- Given some of the unique properties of the number 1, namely 1 divided by itself is still itself.
- Given some of the unique properties of the number 0, namely 0 added to itself is still itself.
- Why couldn't there be a number infinity which is itself whether it is added/mutiplied/divided to/by itself or any other number, just as 0 is itself when multiplied by another number.
- Also, infinity does hold up to some rules of other numbers, infinity/infinity would still equal 1.
So basically, Infinity is a number, until proven guilty.
Some people misunderstood the goal of this writeup, it was meant to illustrate some of the ways in which infinity might seem like a number in order to elicit accurate explanations of why it actually is not a number, rather than the previous writeups which mainly just stated that it was not a number. In any case
ariels was nice enough to point out the
the zero/infinity paradox which helps to explain why it is that x/0 does not equal infinity. For more on why it doesn't make sense to define infinity as a number look to the
I can divide by zero node.