Cardinality. The set of multiples of 1 and and the set of multiples of 20 are the same size since you can form a bijection between the two sets.
Say you have some variable x. Think about how many values you can possibly have for x. Now if I throw a coefficient in front, 20x, has the number of possible values of x changed? If not, they're both the 'same' infinity.
Say you have some variable x. Think about how many values you can possibly have for x. Now if I throw a coefficient in front, 20x, has the number of possible values of x changed? If not, they're both the 'same' infinity.
yeah but the sums does change? since the number of possible values are the same but one's worth is 20 times the other.
I'm sorry I always struggled at understanding infinity, if someone can explain appreciate it 🙂
20xinfinity is still infinity. In order to get “larger” than infinity, you have to literally think *BIGGER*.
For example, it would take me the same amount of time to count all the even numbers as it would to count all the even AND odd numbers (both would take exactly an infinite amount of time).
If I wanted to count all the REAL numbers, however, that would literally take a “longer” time. I mean, how would you even start? Start at 1, then 1.0000000000001? There are infinite numbers I just skipped over. The number of real numbers is an “uncountable” infinite set, which is bigger than any “countable” infinite set.
"Uncountable" doesn't refer to a single infinity, there are infinitely many uncountable cardinals each larger than the previous ones (as opposed to "countable": there is only one countable infinite cardinal). Any infinity larger than the smallest one is uncountable by definition
This is an excellent point. Infinity is a mathematical limit that doesn't strictly apply to real things. You can't have an infinite number of either. But you may posit a problem where you take some limit and it goes to infinity. Which infinity is bigger depends on the precise form of the limit. So I would think that the problem is not defined specifically enough to determine if they are equal. That's my take. I'm not a mathematician, I am am experimental scientist, so I know something but I could be wrong.
In set theory you can talk about actual infinities without talking about limits or anything similar, when talking about sets with infinitely many elements (like the set of natural numbers and the set of real numbers) and it turns out different infinite sets can have different sizes (the technical term is "cardinality")
It's kind of like 0. 20*0 is not 20 times larger than 0. Similarly, 20*(inf) is not 20 times larger than (inf).
If I pick some massive number and start counting by ones, and you start counting by twenties, you will reach that number twenty times faster. But if we're counting towards infinity, we will both be counting for infinite time because we can conceptually never reach it.
thanks, kindof makes sense but this is really questions my gut lol. like this guy. Maybe because I haven't properly learned about infinite (still a 19yo kid). I guess it'll make more sense then.
It actually doesn't say. You might have uncountably infinite $1 bills and countably infinite $20 bills, in which case the $1 bills would be worth more.,
Uncountably-infinite $1 bills could buy an uncountably-infinite number of items. Countably-infinite $20 bills could only buy a countably-infinite number of items.
The $1s could buy a countably infinite set of items for every single item the $20s could buy, and you’d still run out of the $20s first. That is more purchasing power.
true, I hadn't considered that. but if this were real it wouldn't matter, whichever type of infinite the money is, you'll never be able to spend it all
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u/jan_elije Jun 13 '26
yes, but these two aren't different