RE: Why is infinity afraid of zero?
October 18, 2011 at 8:54 am
(This post was last modified: October 18, 2011 at 9:00 am by edk.)
There's more than one of those.
Can you count it in an infinite number of steps (countable infinity)?
The number of real numbers, for example, is incomparably larger than the number of integers, because unlike the latter it is not countable (which is to say, if you had an infinite number of fingers on which to count, you would not be able to count all of them).
The number of real transcendentals must be smaller than the number of complex trancendentals (including reals) because if you picked a truly random point on a graph, you would miss the axes with probability 1. Yet the number of both real transcendentals and complex transcendentals is "uncountable infinity".
Infinity is a complicated thing, you need to be specific.
Also, to whoever said dividing by zero gives an unknown result, it doesn't. It is not a defined operation. All we can say about the answer is that it is not a number, because any number * 0 = 0, and ( 1 / 0 ) * 0 would be 1 (if division by zero were valid).
Can you count it in an infinite number of steps (countable infinity)?
The number of real numbers, for example, is incomparably larger than the number of integers, because unlike the latter it is not countable (which is to say, if you had an infinite number of fingers on which to count, you would not be able to count all of them).
The number of real transcendentals must be smaller than the number of complex trancendentals (including reals) because if you picked a truly random point on a graph, you would miss the axes with probability 1. Yet the number of both real transcendentals and complex transcendentals is "uncountable infinity".
Infinity is a complicated thing, you need to be specific.
Also, to whoever said dividing by zero gives an unknown result, it doesn't. It is not a defined operation. All we can say about the answer is that it is not a number, because any number * 0 = 0, and ( 1 / 0 ) * 0 would be 1 (if division by zero were valid).
