- 23 Jan '15 00:34 / 3 editsInfinity - Infinity is undefined, as with an infinite number of hotel rooms I can either put an infinite number of guests in every room, having zero free rooms, or I can put an infinite number of guests in every second room, having an infinite number of free rooms, or I can miss out any finite number of rooms at the start, and still fit my guests in with that finite number of rooms left.

I think claiming infinity is a symbol and not a number is rather dodgy. All numbers are symbols too, and infinity comes up in valid mathematics. If you are worried about saying x=infinity, then let us define x=1/0 - 23 Jan '15 01:00 / 2 edits

So pretending, we have x = 1/0.*Originally posted by iamatiger***Infinity - Infinity is undefined, as with an infinite number of hotel rooms I can either put an infinite number of guests in every room, having zero free rooms, or I can put an infinite number of guests in every second room, having an infinite number of free rooms, or I can miss out any finite number of rooms at the start, and still fit my guests in with t ...[text shortened]... es up in valid mathematics. If you are worried about saying x=infinity, then let us define x=1/0**

What is 1/0 - 1/0?

Multiply both sides by 0. Eliminates the 0's.

We have 1-1.*

What is 1-1?

0.

Ergo, x-x=0 even when x=1/0 in the pretend world.

*Edit: or we have 0-0 at the starred equation. Same outcome.