infinity is when I count to 1 million and get bored of counting

It is the simply the concept of endlessness, trying to use infinity in mathematical equations just ends up completely breaking math.

It can be a little more than that, for example as seen earlier, there are different kinds of infinites and we have tools to compare them.
Also you will find many mathematical equations using infinity, for example when working with limits or cardinalities.

When comparing infinites, it really boils down to understanding why the bijection is the correct tool and from there all these other questions will feel redundant

Yeah, I moreso meant trying to use infinity as a constant in basic arithmetic or algebra. That's how Enkevah was trying to use it.

Infinity is not the expression of a number, but the expression of a limit. Although the value of a number or a function cannot be infinite.
This means that, sometimes, it will be possible for us to use infinity as if it were just another value, and perform operations with it. To do this, we must always keep in mind the underlying idea of limit and, furthermore, that infinity is the limit of any other real number.

Infinity is not the expression of a number, but the expression of a limit.

It is neither. But a function or sequence may have infinity as its limit somewhere.

Although the value of a number or a function cannot be infinite.

Of course a function can be infinite, just not a function that has the real numbers as its range, which is probably what you are used to.

This means that, sometimes, it will be possible for us to use infinity as if it were just another value, and perform operations with it.

I think i see where you got this from. You are talking about functions within a limit expression. When we see a term like
lim(x->0) (g(x)/f(x)) or anything like that, we may say g goes to infinity or f goes to infinity with x -> 0, however it is important to note that when you are performing any arithmetics on these functions, you are not dealing with infinities. The limit is applied at the end, you are just performing arithmetics on normal numbers or functions.

i don't think we need aleph numbers to answer tacky's question fwiw

nonononono

is roughly where the thread should've ended

Edited 10/16/2024 00:11:15

infinity is a lot powerful than people realize or think. doesnt hurt to discuss

the scientific illiterate are people too ;)

https://youtu.be/jzy2dgEUOhY

I think the only way to settle this thread is to call the true expert: Buzz Lightyear. That toy knows what's beyond infinity.

lmao. to infinity and beyond!!

Can you guys check my math here?

2 order delay cards out-delay 1 order delay card. Therefore:

2*(infinity) > 1*(infinity)

Divide both sides by 2; on the left you remove the coefficient, on the right it has previously been stated that using operations on infinity breaks math, so:

infinity > broken stuff

since tacky's arguments also equal broken stuff, we can substitute:

infinity > tacky's arguments

Therefore, literally everything is better than tacky's arguments

Q.E.D.

wait so why is infinity divided by 2 smaller, but infinity + 1 is the same?

I'm not trying to spoil anyone's fun, but for those who are curious, playing two Order Delay Cards will get you to the "ordinal" number 2w. Ordinal numbers are about order. (By w I mean the Greek letter omega. It is the smallest infinity, from amongst the ordinal numbers.) The next moves are numbered 2w + 1, 2w + 2, etc. So w is "infinity", but only a particular infinity -- and one of many.

As a different example, suppose you make some moves, which I'll number 0, 1, etc. Then you play an Order Delay card, then make moves we can number w, w + 1, etc. As we all know from experience, it doesn't matter how many moves you made in the first phase, this will not affect the move list in the next phase. So, 1 + w is just the same as w, for example. In other words, making two moves and then playing the card (or, "skipping an infinite number of moves") gets you to the same point as just playing the card. Put another way, making delay moves in the first phase has no effect on the move order in later phases.

On the other hand, playing the card and then making a few moves, does not get you to the same point as just playing the card. So w + 1 is not w!

[The situation is different for "cardinal" numbers. All the infinities mentioned above have the same size in this sense, that is, the same cardinality. This size is written aleph_0, where aleph is the Semitic letter for "a". This is the smallest infinity, for the cardinal numbers.]

Wow what a genius. 1 + infinity is the same as infinity, but infinity + 1 is totally different :o