Someone smarter than me please figure this out

[Chiboko]

First of all I'm going to start of with this argument:

1/0.5 = 2

1/0.25 = 4

1/0.125 = 8

In such a sequence as the value being divided by approaches 0, the end value approaches infinity. Using such logic (though it is not necessary to the rest of this argument) any number divided by 0 could arguably equal infinity. This is simply back story, the rest goes like this:

Where 'X' can equal any finite number:

X*10^-infinity

The resulting number (for simplicity sake X=1) is a 1 with an infinite number of zeros in front of it. This is a technically finite number that is larger than 0 while at the same time being infinitely small. Practically speaking this number is 0 while in fact it is actually slightly higher than 0 by an infinitely small mount.

If we divide 'Y' (any finite number which for simplicity sake is also 1) by the number that was just made then using the logic at the top of this post, since the previous number is infinitely small without being 0; by dividing by it we get another number that is infinitely large while still technically being a finite (not infinity) number.

The end result is that we have two numbers that are functionally identical to '0' and 'infinity' without actually being either of them. They are also both technically finite numbers yet they cannot be written down.

Feel free to: Discuss, point out holes in my logic, base new forms of propulsion on this logic

[razark]

The limit of 1/x as x approaches 0 from the positive side is infinity. The limit as x approaches 0 from the negative side is negative infinity.

So, is your "infinity" from 1/0 positive or negative?

(And this is why calculus is based on dividing by 0.)

[Dust]

There is finite and there is infinite. In your sequence, if you look at any individual step n - no matter how large - n will be finite, so the result will be finite. There is no step where n=infinity. Infinity only comes into play when you imagine if this were to go on for an infinite amount of time - but as far as I'm concerned infinity never happens. So no matter how far you go in this sequence each step always results in a finite number - and the reciprocal of that number is also finite.