Thread:C1932/@comment-44038403-20200622162544/@comment-44038403-20200627040639

Turns out 1/inf may actually not be 0.

Infinity is no number.

Please read it again and again until you understand. No offense, but this concept we really must understand before we can advance. Infinity is not a number, and you can't do straightforward arithmetic calculations w/ infinity.

To illustrate the nonsensical jam that one gets in when they say 1/inf = 0, consider replacing the denominator with any other number....an ACTUAL one.

1/2 = 0.5

Now I don’t think that anybody would find this statement very controversial. And we can multiply the quotient by the divisor to yield the dividend in another true, non-controversial statement:

0.5 x 2 = 1

So what happens if we attempt to prove that 1/inf = 0?

We get an invalid statement;

0 x inf = 1

Which has no sensicality whatsoever.

First of all, zero times any number yields zero, so if we’re going to treat infinity as a number, then zero times infinity should not be equal to 1.

Otherwise, even if we WERE going to treat infinity as a number, I could get it if you wanted to argue that infinity times anything is still infinity.

Thus, if we attempt to claim that zero times infinity is one, being a logical extent of 1/inf = 0, we'd end up contradicting ourselves atrociously.

What you want is a limit. Such allows us to explore what a certain value trends towards.

lim 1/x = 0 x>∞

To clarify about it, as x gets larger and larger, 1/x gets smaller and smaller. If you could evaluate 1/x for larger and larger values of x, you would near zero, until time's end. But this statement is NOT implying 1/inf = 0.