A Jumble of Thoughts

There are different kinds of infinity, and some are larger than the others.

Essentially, there is a countable infinity, and an uncountable infinity.

Countable infinity is what  we all typically think of when we hear the term”infinity.” For example, you start counting at 1, and then eventually get to big numbers like a million,  billion, trillion, etc.

Uncountable infinity is, on the other hand, is an infinite set that has too many elements to render it countable. It’s impossible to count how many there are, because it’s impossible to find the “starting number” in the first place.

It doesn’t even stop there! There are infinities that exist for power sets, and power sets of infinite sets, subsets, all kinds of sets!

Then we have real numbers and natural numbers. Natural numbers are also infinite, but significantly less so compared to real numbers. And as noted in an old Reddit thread, “there are as many real numbers as there are subsets of the natural numbers, so the power set of the naturals is as large as the set of reals.”

So when you take the power set of the real numbers, you’ll end up with something that’s even bigger than uncountable.

Amazing, right?

There are certain groups of professionals who feel that infinity is merely a lazy mathematical concept, and there are physicists claiming that the concept of infinity is ruining physics.

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Math and physics. These two tribes are constantly arguing about infinity, making it a rigorous concept to discuss. When mathematicians and physicists argue about something, it usually goes nowhere because what might be theoretically correct for math can also be practically correct for physics. And…

Wait. Infinity. Tea. My favourite tea shop is named InfiniTea! 😀

Speaking of tea, is it time for lunch? I’m hungry. >.<

…basically, this is what happens when I start introspecting.

I hate it, I prefer taking action to thinking, although sometimes I will think of something interesting like this that will hopefully keep me occupied for a few minutes.

Then I’ll be bored again and start being restless unless I do something.

Anyway, I’m going to play some Pokemon now. I hope you guys have a nice day!

PS: discrete mathematics is not a good university subject to invest in, just take geometry or something.

PPS: Wolfram Alpha will save your ass in Uni, so use it.

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