Is infinite really infinite? ( and why fractions bug me )

Citizen Empire

Family
Founder
Feb 4, 2013
232
2
18
City of Ashes
Well yeah, it's defined ( limitless or endless space ), in fact there are even an infinite number of infinities. Take for instance 1 & 2. Seems rather short, right? Not allot of wiggle room? Well think again, in fact, the space between is infinite. No really.
what's between 1 & 2?( 1.5 )
1 & 1.5 ( 1.25 )
Any number in between 1.25 & 1 ( ... 1.1 )
keep going ( 1.01)
( 1.001, 1.00001, 1.0000000000000000000000000000000000001, 1.12, 1.20 ) [ Yes, I'm skipping around ] But still, you can keep going.

And that's what bugs me; how can there be infinite space when you know the end? Which then brings back the question; is infinite really infinite?
 

Shadbot

Noob
May 23, 2014
3
0
1
I live at my comptuer
Well you see do you really know the end of the infinite between 1 and 2?
The way you defined your infinite as
between 1 & 2?
you aren't ending on the number 2 You are in fact ending just before 2, but what is the number just before 2? It isn't 1.99999... as I can prove. So what is it then? It is a number with one less than infinite nines.
And it isn't that there is infinite space between the numbers but an infinite possible number of divisions.
 

Shadbot

Noob
May 23, 2014
3
0
1
I live at my comptuer
Alright so to clarify my previous post, and to go back to some of the points that I didn't cover well in your original post. So the question is "is infinite really infinite?". This can be interpreted in different ways. There is the infinite between one and two and the infinite between zero and, well, infinity. The infinite between two defined numbers is often confusing as people can't see the infinite between them. See the numbers between one and two are an infinite set of numbers, and an infinite set is in fact just a set of numbers that is not finite. In fact this is known as an uncountably infinite set as there are too many numbers to possibly count, whereas the set from zero to infinity is known as a countable infinite set as it is theoretically possible to count each number in it. Uncountable infinities are possible as there are numbers that don't end ever. In fact there are far more infinite decimals than there are finite decimals (both infinite though). So there is another infinity inside an infinity inside an infinity. All of which are infinite.