# Which infinity is the biggest infinity?

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• #186148
Anonymous
Guest

>Some infinities are bigger than other infinities
But which one is the biggest infinity?

• #186149
Anonymous
Guest

the number when your mom steps on the scale

• #186150
Anonymous
Guest

∞^∞

• #186154
Anonymous
Guest

∞^∞^∞

• #186155
Anonymous
Guest

Can you exponent an exponent? How the fuck does that even work.

t. my degree is my high school diploma

• #186156
Anonymous
Guest
• #186157
Anonymous
Guest

>fraction calculators
Duck duck go is dumb, though exponenting an exponent didn’t turn up anything useful either

• #186158
Anonymous
Guest

better off with this example

where n = 2
just replace 2 with ∞

• #186160
Anonymous
Guest

[math]sum _{n=0}^{infty }:left(infty -nright)^{infty ^{infty ^{infty ^{infty ^{infty …}}}}}[/math]

• #186151
Anonymous
Guest

The Lord.

• #186153
Anonymous
Guest

1/0
Correct. He doesn’t exist.

• #186159
Anonymous
Guest

woke af church kleene ordinal

• #186170
Anonymous
Guest

What about the Church Kleene ordinal relativized to [math]0^{sharp}[/math]?

• #186291
Anonymous
Guest

>faithful remilia poster
Bless you.

• #186152
Anonymous
Guest

the set of all infinities

• #186212
Anonymous
Guest

[…]

You can still +1 on the bigger one. It doesn’t exist, same as the smallest number.

• #186284
Anonymous
Guest

but that set will by definition include all those.

• #186162
Anonymous
Guest

There is no biggest infinity, in the same way that there is no biggest natural number.
You can go with aleph(aleph(aleph(aleph(aleph(…))))) forever.

• #186163
Anonymous
Guest

feet

• #186165
Anonymous
Guest

>>Some infinities are bigger than other infinities
Nope.

• #186166
Anonymous
Guest

>>Some infinities are bigger than other infinities
Yup.
>>What is mafs

• #186172
Anonymous
Guest

yes, scrotebrain. Imagine two signals, just recurring beeps, that go on forever. One beeps every minute forever, one beeps every second forever. They’re both infinite but the latter is clearly many times more beeps.

• #186175
Anonymous
Guest

You are literally wrong. The number of natural numbers divisible by 60 is equal to the number of natural numbers.
X = {x | x = 60n for n e N}
It’s not hard to see how this is a bijection, and therefore proves that X and N have the same cardinality.

• #186176
Anonymous
Guest

>steel is heavier than feathers

• #186177
Anonymous
Guest

Is an infinite amount of steel heavier then an infinite amount of feathers?

• #186186
Anonymous
Guest

No

• #186171
Anonymous
Guest
• #186174
Anonymous
Guest

My infinity is bigger than your infinity, true for all (you’s)

• #186178
Anonymous
Guest

"Some infinites are bigger than other infinites".

That’s false.

What sense does it make to say one infinity is larger than another? To be infinite is to have no maximum. There is no larger "No maximum".

Lets pretend we have two bags that can hold infinitely many objects. You’ve somehow managed to convince yourself that you can fill up one of those bags then empty it and fail to fill up the second bag with the emptied objects. That’s not how ‘infinite’ works.

• #186179
Anonymous
Guest

imagine all the counting numbers-1, 2, 3, 4, etc. that’s infinity type one Imagine a bag that can hold all of them.

now let’s imagine infinity type 2-that’s all the fractions between all the numbers. using only the fractions between 0 and 1, i can fill up that first bag of type one infinity, and still have all the other infinite fractions between the other numbers to go.

• #186182
Anonymous
Guest

You can’t "fill up" a bag that has no maximum of how much it can hold. If you’re claiming to have "filled up" the bag then the implication is that there was a "last" piece of space that got filled and there’s not. What you’re doing is dishonest manipulation of words.

There is ALWAYS space left over in bag that has no maximum of how much it can hold. You can always fit more in.

• #186183
Anonymous
Guest

you’re clinging to the semantics of this thought experiment very tightly right now and it’s not a great look-the fact is that i can match every single number in the naturals with a fraction between 0 and 1. The "bag" is clearly not a real thing, it’s just a metaphor I went ahead and invoked since you brought it up.

Do you think that the cardinality of all the fractions is the same as the naturals? Because ot me that seems totally nonsensical given how simple the matching counter-example is.

• #186185
Anonymous
Guest

Lets imagine you pick a random number from the set of real numbers and one from the natrual numbers and swap them. The implication is that you’ll "run out" of natrual numbers before you’re able to swap the two sets.

Ask yourself: " Does this make sense? "

There is always another natrual number.

You can’t "run out"

• #186187
Anonymous
Guest

can i match every single natural number with a fraction between 0 and 1?

• #186191
Anonymous
Guest

This is the bullshit trickery i’m talking about. You can manipulate how you "match" numbers. Can i "match" fractions between 0 and 1 with only natrual numbers that start and end with one with only zeros between them?

101 1001 10001 then 202 2002 20002 then 3 and so on.

You can contruct infinitely many "unique" natural numbers using words and "match" them however you want.

• #186192
Anonymous
Guest

you haven’t answered the question though

• #186195
Anonymous
Guest

I did. I said you can contruct infinitely many sets of unique natural numbers and match them however you want.

You can match fractions from 0 to 1 with 1234… or 10,1001… or 12012, 120012.. or 707,7007… or 121,1221.. etc. So what?

• #186189
Anonymous
Guest

>"run out"
hand waving intensifies

• #186181
• #186184
Anonymous
Guest
• #186188
• #186190
Anonymous
Guest

>To be infinite is to have no maximum. There is no larger "No maximum"
>To be a banana is to be yellow. There is no larger "Yellow"

• #186193
Anonymous
Guest

>To be a banana is to be yellow. There is no larger "Yellow"

Incoherent babble

• #186194
Anonymous
Guest

just as
>To be infinite is to have no maximum. There is no larger "No maximum"

• #186196
Anonymous
Guest

Is there a maximum natrual number.

I only want a yes or no.

• #186197
Anonymous
Guest

No

• #186198
Anonymous
Guest

So there is "no maximum"? Right?

• #186199
Anonymous
Guest

maximum of what?

• #186200
Anonymous
Guest

Maximum number of times you will take the bait.

• #186202
Anonymous
Guest

There is not "last" element you bafoon.

You can’t "run out" of natural numbers.

You can create infinitely many sets of unique natrual numbers and then create more unique natural numbers with that set then infinitely many more with the new sets

• #186203
Anonymous
Guest

so?

• #186204
Anonymous
Guest

"So?"

Huh?

• #186205
Anonymous
Guest

how is that relevant to some infinities being larger than other infinities

• #186206
Anonymous
Guest

Because some infinites aren’t larger than other infinities otherwise they’re not really infinite.

• #186207
Anonymous
Guest

Lol. Then why can’t you map the reals onto the integers, you giant scrote?

• #186209
Anonymous
Guest

I don’t have to map shit you freaking idiot.

Infinite is infinite. It doesn’t if you can play wome word games that lead to confusion.

• #186210
Anonymous
Guest

>I don’t have to map shit
Yes, you do. If we’re talking about identical amounts, there is a one-to-one mapping.

• #186211
Anonymous
Guest

>I don’t have to map shit
how else would you compare two amounts?

• #186213
Anonymous
Guest

We’re not comparing " 2 amounts" we’re comparing infinities.

With just 101,1001, i can create infitley many sets of infinite natrual numbers. Where the fuck do you "run out"?

101 then leads to 1010101, 10100101, then 1010010010100101 and so on. You literally can’t run out. The numbers inbetween can literally be any number. You’d have to be a complete moron to think there are somehow "less" natrual numbers than real numbers.

• #186214
Anonymous
Guest

>We’re not comparing " 2 amounts" we’re comparing infinities.
Since you reject the normal method of comparison, by what token can you compare infinities, you scrote?

• #186215
Anonymous
Guest

You can’t "compare" infinites you freaking moron. You can’t ask " these two bags have no maximum item limit, which one has a higher maximum limit?

Imagine we stack cubes. For every natrual number we add one cube and the same for every real number. The implication is the one tower will be taller than the other.

• #186216
Anonymous
Guest

>You can’t "compare" infinites
Then why are you telling me all infinities are the same?

• #186217
Anonymous
Guest

Because something is the same as itself you scrotebrain.

Is 5 the same as 5? Are there 5s that are bigger than other 5s?

• #186218
Anonymous
Guest

How do you know the size of the set of the natural numbers, and the size of the set of the real numbers, is the same? Calling both of them "infinity" doesn’t prove it, scrotelord.

• #186220
Anonymous
Guest

Does how you "choose" to "map" infinites
Affect the results you get?

• #186221
Anonymous
Guest

Why are you deflecting? I asked you a question: how do you know the size of the set of the natural numbers, and the size of the set of the real numbers, is the same? By what rule do you determine their equality?

• #186222
Anonymous
Guest

By the fact that you can’t "run out" of natrual numbers. Either you can run out of them or can’t. Which is it?

You can’t run out of natrual numbers and tou can’t run out of real numbers therefore there’s not "more" of one than the other.

• #186224
Anonymous
Guest

>By the fact that you can’t "run out" of natrual numbers
I didn’t say anything about "running out" of anything.

>You can’t run out of natrual numbers and tou can’t run out of real numbers
So what? Why does that constitute "equality"?

• #186226
Anonymous
Guest

what sense does it make to ask about the equality of objects that can have no end?

Answer my question and i’ll be done. Is a tower stacked with natural numbers "shorter" than a tower stacked with real numbers? One block for every element in the sets.

• #186229
Anonymous
Guest

>what sense does it make to ask about the equality of objects that can have no end?
So are you saying the sizes of infinite sets can’t be compared at all, or that the sizes of all infinite sets are equal?

• #186231
Anonymous
Guest

Yes

• #186232
Anonymous
Guest

So which one is it, scrote? Are they equal, or are they incomparable? These two positions are mutually exclusive by definition.

• #186233
Anonymous
Guest

>Is a tower stacked with natural numbers "shorter" than a tower stacked with real numbers? One block for every element in the sets.

• #186235
Anonymous
Guest

The answer is a trivial ‘no’. What does it have to do with anything? No one is defining equality in terms of the heights of towers of blocks, scrotelord.

• #186237
Anonymous
Guest

>no

There you go.

I’m done here

• #186238
Anonymous
Guest

Yes, you’ve proven that comparing the heights of blocks of towers doesn’t work when the height is undefined. Well-done refuting your own scrotebrained idea.

• #186239
Anonymous
Guest

Yes, it’s shorter.

• #186240
Anonymous
Guest

Sounds like you’re every bit as scrotebrained as him.

• #186241
Anonymous
Guest

>I have no argument

• #186242
Anonymous
Guest

>comparing the sums of divergent series

• #186243
Anonymous
Guest

who is comparing sums of divergent series?

• #186244
Anonymous
Guest

scrotebrains talking about the heights of towers made up from infinite blocks.

• #186245
Anonymous
Guest

the heights are not well defined, but one can say that the real number tower is higher than the natural number tower

• #186249
Anonymous
Guest

>divergent series have no defined sums, but we can say that the sum of one divergent series is larger than the sum of another

• #186250
Anonymous
Guest

why are you still talking about divergent series?

• #186252
Anonymous
Guest

scrotebrains talking about the heights of towers made up from infinite blocks. You’re clearly mentally ill.

• #186253
Anonymous
Guest

I’ve told you. The heights are not well defined, but that doesn’t mean one cannot says that one tower is higher.

• #186254
Anonymous
Guest

>The heights are not well defined
Then what do your imaginary comparisons have to do with mathematics?

• #186255
Anonymous
Guest

Everything

• #186256
Anonymous
Guest

Mathematics doesn’t deal with things that are "not well defined". Sorry.

• #186257
Anonymous
Guest

That’s what I’ve said. The height is not well defined.

• #186258
Anonymous
Guest

>my infinite towers analogies have nothing to do with mathematics
Okay. Glad we have that settled.

• #186259
Anonymous
Guest

yes, it does. one tower is higher than the other.

• #186260
Anonymous
Guest

>one tower is higher than the other in my imaginary schizo universe that has nothing to do with mathematics
Yes, glad we agree on everything.

• #186261
Anonymous
Guest

no, one tower is higher than the other in a perfectly valid mathematical sense.

• #186262
Anonymous
Guest

>i’m a mouth-breathing imbecile
Yes, that’s exactly what I’m saying. Thanks. We can end this discussion here.

• #186263
Anonymous
Guest

why are you resorting to insults?

• #186264
Anonymous
Guest

Not an argument.

• #186265
Anonymous
Guest

>>i’m a mouth-breathing imbecile
>Yes, that’s exactly what I’m saying. Thanks. We can end this discussion here.
is an argument?

• #186266
Anonymous
Guest

Still not an argument. Sorry. Can you come up with a decent argument next time?

• #186267
Anonymous
Guest

I have plenty of arguments. it’s impossible to present them when you keep shoving words into my mouth though.

• #186268
Anonymous
Guest

Nope, that was still not an argument. I guess you just don’t want to have a courteous and civilized discussion.

• #186269
Anonymous
Guest

>I guess you just don’t want to have a courteous and civilized discussion.

>Sounds like you’re every bit as scrotebrained as him.
>You’re clearly mentally ill
>>i’m a mouth-breathing imbecile
:^)

• #186270
Anonymous
Guest

Was that an argument? I don’t think so. Too bad, I really wanted to have a civilized discussion with you.

• #186271
Anonymous
Guest

then why did you insult me without any reason?

• #186272
Anonymous
Guest

Nope, that’s not an argument, either. I’ll be here when you’re ready to engage in the discussion like a big boy instead of indulging in personal drama.

• #186273
Anonymous
Guest

I am. just stop insulting me and shoving words into my mouth.

• #186274
Anonymous
Guest

That was not an argument, nonny.

• #186275
Anonymous
Guest

of course not. why should I give you any argument when you clearly don’t want to hear it?

• #186276
Anonymous
Guest

>why should I give you any argument
See? You’re not a rational or civilized person at all.

• #186277
Anonymous
Guest

>You’re a rational or civilized person
thank you 🙂

• #186278
Anonymous
Guest

That’s not an argument, either.

• #186279
Anonymous
Guest

>That’s an argument
I don’t think it is, but thanks for finally agreeing with me

• #186281
Anonymous
Guest

Nope. Still not an argument.

• #186282
Anonymous
Guest

>Yes. Still an argument.
stop it, you’ve already acknowledged that you were wrong

• #186283
Anonymous
Guest

>i’ve already acknowledged that i breathe through my mouth
ok

• #186285
Anonymous
Guest

>ok
thanks

• #186225
Anonymous
Guest

do you compare numbers by the fact that you can run out? 4=5 because both run out?

• #186227
Anonymous
Guest

You could say that x>y if you "run out" of y first, x<y if you "run out" of x first, and x=y if you "run out" of both simultaneously. Unfortunately, that doesn’t work for infinite sets, because you don’t run out of anything and the guy is a giant scrote.

• #186228
Anonymous
Guest

Yes. The fact that they run out is very important. I can ask if i can run out of one before the other to compare them. If i run out of one before the other i know its ‘less’

• #186230
Anonymous
Guest

That’s nice, but how do I know they’re equal using your "running out" system, scrotelord?

• #186236
Anonymous
Guest

>. I can ask if i can run out of one before the other to compare them. If i run out of one before the other i know its ‘less’
this is extra condition. why do you not allow extra conditions for infinite sets?

• #186223
Anonymous
Guest

>I’m gonna pretend the quantification is universal instead of existential to derive contradiction

• #186219
Anonymous
Guest

infinity is an amount

• #186208
Anonymous
Guest

prove it

• #186180
Anonymous
Guest

100

• #186201
Anonymous
Guest

Are there any practical uses of infinity? I know you can use algebra, trigonometry, calculus in the real world for calculations but what would you use infinity for?

• #186234
Anonymous
Guest

Real numbers were a mistake, take the wildberger pill.

• #186247
Anonymous
Guest

woke af

• #186246
Anonymous
Guest

[…]

This deserves special attention because Cantor is the biggest meme on the planet. Mathematicians really wanted real numbers to work out so they listened to a literal schizo. Here is a quote from him:
"""
I have never proceeded from any Genus supremum of the actual infinite. Quite the contrary, I have rigorously proved that there is absolutely no Genus supremum of the actual infinite. What surpasses all that is finite and transfinite is no Genus; it is the single, completely individual unity in which everything is included, which includes the Absolute, incomprehensible to the human understanding. This is the Actus Purissimus, which by many is called God.
I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author. Thus I believe that there is no part of matter which is not — I do not say divisible — but actually divisible; and consequently the least particle ought to be considered as a world full of an infinity of different creatures.
"""

This is clearly not from a man who is mentally well. Even with 21st century technology, nature doesn’t really have an infinities we can definitely prove. Meanwhile, this lunatic in the 19th century was claiming that there is infinity everywhere in nature.
Aristotle was correct; there are only potential infinities, not """actual infinities""".

• #186289
Anonymous
Guest

npc’s fingers wrote this.

• #186292
Anonymous
Guest

>uses the most generic wojak on the planet
>calls someone else an npc
this is pure, undiluted cope. also, an npc believes whatever else everyone else believes. since most mathematicians (and I’d even say most lay people), consider the set of natural numbers to be a valid mathematical object, your response doesn’t even make sense.

• #186290
Anonymous
Guest

>Aristotle was correct; there are only potential infinities, not """actual infinities""".
this is like Einstein’s quote about either everything being a miracle or nothing being a miracle

• #186248
Anonymous
Guest

[…]

woke af

• #186251
Anonymous
Guest
• #186280
Anonymous
Guest

[…]

[…]
This deserves special attention because Cantor is the biggest meme on the planet. Mathematicians really wanted real numbers to work out so they listened to a literal schizo. Here is a quote from him:
"""
I have never proceeded from any Genus supremum of the actual infinite. Quite the contrary, I have rigorously proved that there is absolutely no Genus supremum of the actual infinite. What surpasses all that is finite and transfinite is no Genus; it is the single, completely individual unity in which everything is included, which includes the Absolute, incomprehensible to the human understanding. This is the Actus Purissimus, which by many is called God.
I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author. Thus I believe that there is no part of matter which is not — I do not say divisible — but actually divisible; and consequently the least particle ought to be considered as a world full of an infinity of different creatures.
"""

This is clearly not from a man who is mentally well. Even with 21st century technology, nature doesn’t really have an infinities we can definitely prove. Meanwhile, this lunatic in the 19th century was claiming that there is infinity everywhere in nature.
Aristotle was correct; there are only potential infinities, not """actual infinities""".

Blow it out your ass Wildberger cuck.

• #186286
Anonymous
Guest

seething

• #186287
El Arcón
Guest

I am the biggest one.

• #186288
Anonymous
Guest

The question wasn’t who the biggest scrote ITT is.

• #186293
Anonymous
Guest

>>Some infinities are bigger than other infinities
complete and utter schizophrenia.
Hitomi theory solves all of this.

• #186294
Anonymous
Guest

[…]

woke af and Cantor-Schroder-Bernsteinpilled, also witnessed

• #186295
Anonymous
Guest
• #186296
Anonymous
Guest

>all the screeching wildbergers itt
get a life fucktards

• #186297
Anonymous
Guest

>Some infinities are bigger than other infinities
this is false, there is only one infinity
if you subtract infinity by 1 it’s not infinity anymore, it’s "infinity minus 1"
if you add 1 to infinity it’s not infinity anymore, it’s "infinity plus 1"

• #186298
Anonymous
Guest

Are three infinities bigger than two infinities? What about infinite infinities?

• #186299
Anonymous
Guest

If [math]infty := frac{1}{0}[/math] then [math]+infty = -infty[/math]
From there it can trivially be shown that [math]2*infty = infty + infty = infty – infty = 0[/math]
Likewise, [math]3 * infty = 2( infty) + 1 ( infty) = 0 + infty = infty[/math], meaning odd multiples of infinity are infinity and even multiples are zero.

Since [math]infty[/math] is even, [math]infty * infty = 0[/math]
This is irrefutable.

• #186300
Anonymous
Guest

>the biggest infinity?
tRump’s lies

• #186301
theonemirror reflectsitself
Guest

Since a subset of an infinite set is infinite:
Let the subset be human consciousness:
therefore, freewill exists

Infinite choice offers infinite chosen, even if the choice is predetermined

• #186302
Anonymous
Guest

The fifth one

• #186303
Anonymous
Guest

Isn’t the positive infinite bigger than the negative infinite due to the fact that zero is part of the positive infinite? In case I might be wrong correct me.