Infinite infinities

Quoting an-salad

there are an infinite number of infinities.

Cantor beat you to it.

Reply to Banno :smirk:

Reply to 180 Proof it's a pretty cool result that leads on to Gödel's incompleteness and Turing's halting problem.

Reply to an-salad

Transfinite numbers

Don't get lost in the labyrinth.

Reply to Banno :up:

Reply to Banno Are only in theory.

Quoting an-salad

How many decimal numbers are there in between any two whole numbers (such as 0 and 1)?

Infinity.



How many whole numbers are there?

Infinity.



Therefore, there are an infinite number of infinities.

Yes. What's your question?

By the way, I would ask, are you aware that the infinity of the real numbers between 0 and 1 is a different kind of infinity to the infinity of the natural number series? Forgive me if you already knew that; if not, I recommend you google Cantor's Diagonal Argument for the non-countability of the real numbers.

Reply to an-salad
In math we do have different degrees to the vastness of infinities. Some infinities are bigger than others and they can be used to cancel each other out.

That's true. I have read that some high school teachers tell their students that (for example) infinity minus infinity, or multiplied by infinity, or added to infinity, is undefined. Serious disinformation!

Thread is not a philosophical topic.