There Are No "bigger" Infinities

Infinity is not simply a number. It is beyond human comprehension. All the efforts made to actually comprehend infinity have been futile. People say one infinity is greater than other. And they're wrong. Two infinities can only be equal. One cannot be larger than the other. If that's the case then the smaller one has a limit and hence not infinite by definition.

There are there two kinds of infinities. Uncountable and countable. Countable infinity is things that you can start counting but you'll never reach the limit. For example, natural numbers, odd and even numbers.

Uncountable infinity is things you know, can't possibly begin to count. For example the points between the points 0 and 1. There's 0.2, 0.25, 0.627, 0.127, 0.89, 0.99999... and so on. Now repeat the same for all the points on the infinite number line.

Now, you might think that the uncountable set is certainly larger than the countable set since it contains all the elements of the countable set. It's true that it contains the countable set, but that won't make it bigger than the countable infinite set. Simply because both have no true limit to how big the numbers get, they're both equally infinite.

An intuitive way to understand the difference is to consider that the uncountably infinite set is more complete than its countable counterpart. It just has more granularity to it than countably infinite sets. Again, they're both the same in "size".

For further understanding, let's take an example of 2 identical cakes. Assume that each cake represents an infinity. Now we divide the first cake into 100 parts, we can count these 100 parts, thus this is the countably infinite cake. Now, we somehow cut the 2nd cake into infinite, infinitesimally small pieces. This is the uncountably infinite cake since we cannot possibly count the number of pieces. So since both are identical, they're equal in size no matter how many parts we divide it into. While this example isn't entirely accurate, hopefully it's enough to get my point across.

In conclusion, infinite is infinite at the end of the day.

I once went for a stay at Hilbert's hotel. Suckers changed my room all the time. Really annoying.

HAHAHA

looks like a 1st grader to me

Cantor's theorem and diagonal argument nuff said.

Imagine getting debunked by a dead person who lived more than 100 years ago.

your notions of infinity are completely stupid obviously maths is not your thing

Of course there isn't. Infinite is infinite.

Yes.

hahaha yes this guy literally said n{R+} = n{N} because they both are infinite

Exactly.

Lmfao he doesn't even realize that Aleph0 and Aleph1, the cardinality of all natural numbers and all real numbers respectively, are just the tip of an iceberg and that there is an infinite amount of larger infinities.

fat Thor would love that infinite cake example though

yes it is pretty obvious cardinality of C is infinitely greater than R is infinitely greater than N

@darkeryoda: it's not obvious, during my years in university I saw more than one person be rather stumped when introduced to the concept. However, it is true that it's a rather basic set theory notion learnt during first semester.

Pretty sure you can blow this guys mind by explaining what the sum of all natural numbers equates to.

If you mean -1/12, its not as simple, that sum diverges, to reach -1/12 you need to make some choice in your definition of how you are gonna manage infinite series.

If you really wanna be blown away, try calculating the dimension of Cantor's Set, that result blew my mind when studying at uni.

Double posting cause I can't edit my comments...

Not quite, but its getting more and more simple every year.

Ramanujan Summation, for this series, is used in mathematics for rocket science, its in text books, and its in theories for QM, such as the Caimir Effect.

Looking more and more like its actually true.

Imagine getting debunked by meme man

¯\_(ツ)_/¯

this sum works on a falcious result in the series

(1-1+1-1+1-1.....) this series can have two values depending whether number of terms are even or odd but if this series is put in a definitive variable x meaning if this series is assumed to have a definite value and that value is x then after a simple math the sum comes out to be 1/2 but the mistake is sum is not definite it is case dependent .

And also as the other guy sigma(i)[i=1 to i= n] is a diverging series that is its some will come out to be infinite as n tends to infinity so however you see it its value coming out to be -1/12 is not correct at all and also how can the sum of positive real converge to a negative value

There is no "true" maths work by definition it doesn't try to model anything, physics try to make models for reality and use maths for that.

By Ramanujan Summation I assume you mean analytic continuation, extending the series makes it convergent, the regular series is clealy divergent

what do you mean by extending the series

"Infinities" are usually used in mathematics for representation of higher dimensions

Lmao

The person that discovered the notion of uncountable infinities: They are bigger than countable infinities

Random Battleboarder a century later: Naa they are the same size trust me bro

@kemono_dono: why would you ask that? No. I'm not from spacebattles

@lmaolmaolmao: can you prove how one infinity is bigger than the other? And what is the significance of using one infinity over other in battleboarding apart from maths?

@haxxxz: No they aren’t.

Maybe you don't have any bigger infinities, but I do

Yes there are bigger infinities. Get over it.

^ even Ben Shapiro man is smarter than the OP lmao

Its not something simple that I'd like to explain here, if you are interested this channel is the most accesible one that I know at explaining maths beyond high school level, and has a good video on it:

Any individual number in the infinity between 0 and 1 will be smaller than 1 and larger than 0

however, if this infinity is combined together it should be equal in value to any other infinity that is considered a bigger infinity. All the infinite numbers between 0 and 1 combined together are equal to all the infinite numbers between 1 and 2 (a bigger infnity) together. Both are simply infinite.

In that sense, I agree that there is no bigger infinity.

What? No. to begin with, every open subset of the reals has the same cardinality, in particular the full set is open, and thus any given open subset has the same cardinality as the the continuum line, whether its (1,2) or (0.000456456, 0.000789), there's the same amount of elements in both sets.

However, if you take the set of all possible subsets, usually called the power set, it always has a larger cardinality, meaning there is no given set with the "largest" cardinality.

I knew about the zeta function but it is not important for my major so I didn't go deep into that but the problem is the domain of that function since it is a function you give an input and it is ought to give an output but the given output has to be logically true or else it is meaning less putting complex numbers in the domain shows that these results are more of a mathematical findings they have no meaning in real life in my case physics .

and about the cardinality of two sets of real numbers a counter question could be put up:-

lets say f [0,2] -->[0,4] , y = x^2 since this is onto and one one so n[0,2] = n[0,4]

but [0,4] = [0,2] U [2,4] so n[0,4] = n[0,2] + n[2,4]

why this kind of contradictory results arising ?

really? Infinite is infinite? What is the point of this?

"Believe"

@rukelnikovftw:

@rukelnikovftw:about the second one I think you didn't understand what I was saying, simply put I was saying that since you said every open interval on continuum line has the same cardinality

then (0,2) will have the same cardinality as (0,4)

but (0,4) = (0,2] U [2,4) since it is the union of these two sets its cardinality has to be the sum of the cardinality of the two individual subsets since intersection of (0,2] and [2,4) is null.

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about the first say f and g are two functions defined on a region A and f =g for a subset of A then f = g could be extended to the whole region A since isolated 0 s are not possible (or as far as I know) so this result holds true mathematically but logically some wrong results could be obtained .

1+x+x^2.... has a converging interval in (-1,1) but this interval could be extended by writing it in the form 1/(1-x) ( first expression is the binomial expansion of (1-x) ^-1) to R - {1} so by above definition since (-1,1) is a subset of R - {1} then the domain of the first expression could be expanded now lets put x = 3 first expression will yield 1 + 3 +3^2..... and the second expression will yield -1/2

then we are saying that 1+ 3 + 3^2 ..... = -1/2 which is obviously wrong although mathematically true but logically false same goes with zeta function zeta(z) z on continuum line greater than 1 yields expected results for a converging series but before that on the continuum line it does not like the series in hand zeta(-1) = -1/12 = 1+2+3+4... z(negative even integer) = 0 and z from a point other than the real line on the complex plane has no real meaning .

People like mathematicians and scientists do care, but you won't find them on CV.

Because the set of reals cannot be bijected to the set of naturals.

Replace the elements with unit masses and you have battleboard application

Maths is just gay as a whole

@darkeryoda said:

I'll further explain this here since CV is not allowing me to edit comments lately.

The cardinality of [0,2]<R, noted |[0,2]|, is infinity(positive)

|[0,2]| = infinity(p)

|[2,4]| = infinity(p)

|[0,4]| = infinity(p)

Now since infinity is not an element from R when you want to use function with it you cant use the sum defined for R, and since infinity is a limit, we use limits algebra.

infinity(p) + infinity(p) = infinity(p)

So, yes the cardinality of [0,4] is the sum of the cadinalities of its non intersecting subsets, it happens they are all the same. That's the kind of things that happen in infinity, adding not always means having more elements.