what's the difference between infinite and uncountably infinite

[Funnimane]

the way I understand it, infinity is already uncountable by definition, and no matter what you do to it (infinity + 1 or - 1 for example), it's still infinite
so what the balls does "uncountably infinite" mean?
I already know I'm gonna regret asking this

 

[First_Witch]

Its a mathematically proven bigger infinity. The best way to understand it is to look at a example. The set of all natural numbers for example (1, 2, 3 etc) is a infinity. Now look at the set of all real numbers. The amount of numbers in the set of real numbers between 0 and 1 already dwarves the amount of natural numbers. Its called uncountably, because its literally impossible to count the numbers, even when given an infinite amount of time due to how big they are. By comparason, you could theoreticaly count all natural numbers if given a infinite amount of time

 

[Funnimane]

 

[First_Witch]

Oh my, have I lost you?

 

[StekFence]

I thinks it’s basically like, infinity would be stuff like 1,2,3, but uncountable is more becuase you’d have things like, 1.0000000000001,1.0000000000002,1.0000000000003, and these numbers can get infinitely smaller.

 

[Dragoonseraphim]

The way I see it is with whole numbers you can still count them. You will never reach an end but you can still count them(1,2,3,4…). If you include decimals though you can have an infinite number of decimal places. As such after 0 there isn’t a next number to count to as you can keep getting a smaller decimal.

 

[First_Witch]

Right, the set of real numbers include every number. So try to count from 0 to the next smallest number. Is it 0.1? No, real numbers include every number, you can go smaller. And well, you can in fact go infinitly smaller. The next smallest number would be 0.000ad-infinitum1. Its already as big as your smallest infinity and we barely started counting. The difference in size is that big

 

[Vietthai96]

Normal infinite mean you can count to infinity with infinite amount of time. In short, natural number, count from 1 to 2 to 3 to infinity
Uncountable infinite even with infinite amount of time given to you you can count to infinite, it is unreachable infinity, in short, real number. So why, real number unlike natural number have 1.1, 2.5, etc.........thus you need to count those kind of number. From 0 to 1 you have 0.1, 0.2,........0.9 and then 1, however from 0.1 to 0.2 you have 0.11, 0.12,.......0.19 then 0.2, again from 0.11 to 0.12 you 0.111, 0.112.......to 0.119, then 0.12. Again repeat this. Thus even with infinite amount of time, you can't even count from 1 to 2 thus uncountable infinity.
Or another explaination, from 0 to infinity have infinite number, and from 0 to 1 also have infinite number between them. Thus created the formula: infinite^infinite = uncountable infinite

 

[Oblivion_Of_The_Endless]

If you want a more detailed explanation

 

[Arthex]

My brain has been badly damaged by this- oh wait I never had one.

 

[Kowalski]

the way I understand it, infinity is already uncountable by definition, and no matter what you do to it (infinity + 1 or - 1 for example), it's still infinite
so what the balls does "uncountably infinite" mean?
I already know I'm gonna regret asking this

Yes, you are right, basic math operations with infinity is not going to change the quantity of it. “ Infinity “ is usually denoted to Aleph null or Aleph-0, which is basically the cardinality of the set of all natural numbers, for example, X = {1,2,3,4..}. If naturals are not contain within a finite set, counting it would goes on infinitely, since there’ll always be the next number continuing from the previous. Which makes Aleph null a first countable infinite set.

Uncountable infinite set or baseline Low 1-A (dimensions) as you may referred to, the said set was already proven as “ bigger infinite set “ according to the continuum hypothesis. The mentioned set is denoted to Aleph-1, which the set can be thought as the cardinality of the set of all real numbers. Reals are different from naturals, naturals is just regular countable amount, but reals are technically uncountable. Try imagine a line, where there are infinite units go along until the end of the line starting from 0, in between unit 0 and 1 is an infinite decimal expansion because there’ll always be the next decimal next to the previous because it’s the real amount, for example, X = {0.0000…}. This set is technically a bigger infinite set due to the process of infinite decimal expansion. Consequently, this set is called uncountable infinite set because decimals are not countable.

 

[Vietthai96]

Uncountable infinite set or baseline Low 1-A as you may referred to, the said set was already proven as “ bigger infinite set “ according to the continuum hypothesis. The mentioned set is denoted to Aleph-1, which the set can be thought as the cardinality of the set of all real numbers. Reals are different from naturals, naturals is just regular countable amount, but reals are technically uncountable. Try imagine a line, where there are infinite units go along until the end of the line starting from 0, in between unit 0 and 1 is an infinite decimal expansion because there’ll always be the next decimal next to the previous because it’s the real amount, for example, X = {0.0000…}. This set is technically a bigger infinite set due to the process of infinite decimal expansion. Consequently, this set is called uncountable infinite set because decimals are not countable.

Aleph-1 is Low 1-A????, where did you get that???

 

[Oblivion_Of_The_Endless]

Aleph 1 dimensions is Low 1-A*

 

[Vietthai96]

Aleph 1 dimensions is Low 1-A*

Well it is because of dimension though........................

 

[Kowalski]

Low 1-A | Low Outerverse level: Characters who can universally affect, create and/or destroy structures and expanses of uncountably infinite dimensions, or which have a size roughly analogous to them, such as uncountably infinite sets of hierarchical layers or planes of existence, most specifically ones whose amount of layers is comparable to the set of all real numbers,

Aleph-1 is Low 1-A????, where did you get that???

“ and are thus equated to the first uncountably infinite cardinal, ℵ1, for simplicity's sake. “

 

[Oblivion_Of_The_Endless]

Low 1-A | Low Outerverse level: Characters who can universally affect, create and/or destroy structures and expanses of uncountably infinite dimensions, or which have a size roughly analogous to them, such as uncountably infinite sets of hierarchical layers or planes of existence, most specifically ones whose amount of layers is comparable to the set of all real numbers,

“ and are thus equated to the first uncountably infinite cardinal, ℵ1, for simplicity's sake. “

Yes dimensions, not Aleph 1 by itself

 

[Vietthai96]

Low 1-A | Low Outerverse level: Characters who can universally affect, create and/or destroy structures and expanses of uncountably infinite dimensions, or which have a size roughly analogous to them, such as uncountably infinite sets of hierarchical layers or planes of existence, most specifically ones whose amount of layers is comparable to the set of all real numbers,

“ and are thus equated to the first uncountably infinite cardinal, ℵ1, for simplicity's sake. “

uncountably infinite sets of hierarchical layers or planes of existence, most specifically ones whose amount of layers is comparable to the set of all real numbers

 

[Kowalski]

Well it is because of dimension though........................

Yes, but what’s your point here…

 

[Vietthai96]

Yes, but what’s your point here…

My point is that, Aleph-1 alone doesn't mean much

 

[Kowalski]

My point is that, Aleph-1 alone doesn't mean much

Maybe I forgot to mention “dimensions” in my post..

 

[Vietthai96]

Maybe I forgot to mention “dimensions” in my post..

Oh, okay, no problem though

 

[Kowalski]

Oh, okay, no problem though

 

[JmikaelP]

Then, uncountable infinity is best that only infinity?

 

[Vietthai96]

Then, uncountable infinity is best that only infinity?

What do you mean???

 

[JmikaelP]

Its a mathematically proven bigger infinity. The best way to understand it is to look at a example. The set of all natural numbers for example (1, 2, 3 etc) is a infinity. Now look at the set of all real numbers. The amount of numbers in the set of real numbers between 0 and 1 already dwarves the amount of natural numbers. Its called uncountably, because its literally impossible to count the numbers, even when given an infinite amount of time due to how big they are. By comparason, you could theoreticaly count all natural numbers if given a infinite amount of time

What do you mean???

I mean what First Witch said