OneAndOneIs2

So there are an infinite number of numbers. And half of them are odd, and half of them are even.

I know this was a humourous kind of post...

but just to point out to the more serious (and inquiring) readers that since one cannot even measure infinity, it's an absurd logical loophole to assume any such quantity as "half of infinity." Infinity is a concept - not just a symbol representing a number or a number.

Therefore we cannot carry out any mathematical operations on infinity to prove anything either way.

Hi, thanks, my brain just exploded!

You're welcome :o)

Disclaimer: The content of this post is all my opinion. I cannot guarantee the accuracy of anything I have written.

Not really, when you have an infinite amount of rooms, it means no matter how many people go into the rooms, there will always be more space. If you have an infinite number of guests, it means no matter how many rooms there are, there will always be a guest willing to book a room.

If you have infinite rooms, and infinite guests, then the hotel isn't "full". An infine amount of guests can still fit in the hotel, and there is an infinite amount of guests who will do so. (No, the hotel won't be full after that either, it loops to the beggining of this paragraph.)

Even if you have 2 infinities of guests, there will be enough rooms for everyone.

What does this mean? 2xinfinity=infinity.

Quote from an Indian book to make me look smart...

That is full, this is full
From the full, the full is subtracted
When the full is taken from the full
The full still will remain - Isha Upanishad

Applying most operations on infinity would give you infinity at the end.

A notable exception... Any number divided by infinity = 0. That should be easy to understand. A number divided by a large number = a very small number.

"So if you throw that ball and wait for an infinitely long time... who will catch the ball?"

Neither one would catch the ball.

If you throw a ball an infinite distance, no matter how far away it goes, it will never stop flying.

If someone is an infinite distance away from away you, no matter how long you throw a ball, it will not reach them.

Even after an infinite amount of time, the ball will keep flying, and it will still not have reached either of those two people.

You cannot apply many operations to infinity, though there are a few that you can. For example.

There is a dot and there is a line. Every second, the dot moves half the distance between the dot and the line towards the line. It does this an infinite amount of times. At "infinity" the dot would have touched the line. The dot will never go past the line.

How does that work? Does that mean that the dot stops once it reaces the line?

Short answer... yes.

Long answer... no. Think about it this way, since it moves half the distance between the dot and the line every second, the dot is slowing down as it approaches the line.

So while it is extreemly close to the line, as every second passes, it move a tiny tiny bit towards the line. In our world, this concept won't work, since once the dot molecules and the line molecules are touching, the dot can't move forward anymore.

But in the world of math, it is possible. There is always a tiny little bit of distance between the dot and the line. Why? Because it didn't just ram into the line. It walked halfway up the to line in one second, then halfway up the remaining distance in the next second.

If there was distance between the dot and the line from the start, and the dot halves the distance, then the dot can't possibly ever touch the line.

But at infinity it does touch the line.

Theoretically it never does, and it is moving towards the line every second, but these movements are so miniscule that they are only possible in the world of math where dots can move distances smaller than the radius of an electron.

To most people. "The dot stopped and it touched the line." But we all know that isn't actually what happened

thinking about infinity is very cool and fascinating. Also can be quite counterintuitive and maddening. As a small tidbit, think of rational numbers. A rational number is a number that can be represented by a fraction a/b where a,b are integers and b != 0. So 1/2, 34/7723, -39428934/234234222114997, whatever.

Compare all the rationals with integers in the range 0 to 1. Two integers, but in between them there are an infinite number of rationals: 1/2, 1/3, 1/4, ..., 1/n, ...

Turns out, though, that the number of rationals and integers are the same!

Okay, well, infinity is infinity, right? Well, consider the set of reals, then google "cantor's diagonalization"

After that, google banach-tarski paradox. Or brower fixed point theorem. cool stuff.