Countably infinite means that the set is infinite and countable (i.e. you can start at 1, go to 2, etc etc and never stop) which means you can enumerate the specific elements of the set using the counting numbers.

Examples are natural numbers, integers, fractions, etc.

Infinitely countable combinations of countably infinite sets are also countable, so your comment of “infinitely more combinations of whole numbers” is still countably infinite, so long as you really meant COUNTABLY “infinite.. more combinations of whole numbers”

Uncountably infinite means that the set cannot be enumerated.

For example try to write out all the numbers between 0 and 1 in order. Fine, the first is 0, and the second is 0.1 (or is it 0.01 or 0.001 or 0.0001 or aaaarrrrrgggggghhhhh!)

You get the point. You can’t even THINK about what the second number will be, because no matter what you say, I can find a number between your choice and 0. (I just take your number and divide it in half.)

so uncountable sets are bigger than countable sets (infinitely bigger, it turns out)

There is likely a gospel concept in here somewhere about onmiscience or infinite sacrifice, or something, but I cannot think of one right now.

Those are the concepts. Why does it matter?

Was it not clear that I am a math apostate? How the heck would I know?

I do know that for certain limit theorems, and for real analysi, functional analysis and measure theory this really matters, but I can’t recall the details, and even if I could, the explanations tend to get into the weeds very quickly for any, but the most “iron-rodder” of members of the cult of mathematics.

Hope this makes you grateful that you did not check “math major” when you applied to college.

economics on the other hand….

While I think I understand the concept (i.e., there are infinite whole numbers but infinitely more combinations of whole numbers), I can’t imagine when it would ever be necessary to distinguish infinities. Anyone care to give me the single paragraph explanation?

Good to see you post.

For the record, all those embedded derivatives were the answer to many people’s prayers; they just may have not recognised the divine origin of the financial instruments.

It would seem reasonable to conclude that criticising deriviatives is the moral equivalent of speaking evil of the Lord’s annointed.

That is thin ice you are skating on, my friend.

If Math is comparable to the miracles of Western Christianity, then Economics is surely an African religion. Where else do you go to the spiritualist for advice only to have them sell you a potion for an ailment you didn’t know existed, a lá embedded derivatives.

Hah! These cranks even talk about orders of infinity, AS IF we can really distinguish between countable and uncountable!

Whack-jobs, one and all!