- This topic has 155 replies, 1 voice, and was last updated 7 months, 2 weeks ago by
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>Some infinities are bigger than other infinities
But which one is the biggest infinity? -
the number when your mom steps on the scale
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∞^∞
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∞^∞^∞
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Can you exponent an exponent? How the fuck does that even work.
t. my degree is my high school diploma
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>fraction calculators
Duck duck go is dumb, though exponenting an exponent didn’t turn up anything useful either-
bloody hell..it’s not hard
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[math]sum _{n=0}^{infty }:left(infty -nright)^{infty ^{infty ^{infty ^{infty ^{infty …}}}}}[/math]
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[math]sum _{n=0}^{infty }:left(∞-nright)^∞∞[/math]
Here you go.
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oh, the up arrow symbol doesn’t work
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You stinky coon, you
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>up-arrow
you need to go back
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The Lord.
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1/0
Correct. He doesn’t exist. -
woke af church kleene ordinal
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What about the Church Kleene ordinal relativized to [math]0^{sharp}[/math]?
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>faithful remilia poster
Bless you.
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the set of all infinities
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[…]
You can still +1 on the bigger one. It doesn’t exist, same as the smallest number.
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but that set will by definition include all those.
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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. -
feet
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>>Some infinities are bigger than other infinities
Nope.-
>>Some infinities are bigger than other infinities
Yup.
>>What is mafs -
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.
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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. -
>steel is heavier than feathers
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Is an infinite amount of steel heavier then an infinite amount of feathers?
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No
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My infinity is bigger than your infinity, true for all (you’s)
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"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.
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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.
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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.
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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.
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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? "
The answer is no.
There is always another natrual number.
You can’t "run out"
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can i match every single natural number with a fraction between 0 and 1?
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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.
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you haven’t answered the question though
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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?
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>"run out"
hand waving intensifies
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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.
freaking owned
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There is ALWAYS space left over in bag that has no maximum of how much it can hold. You can always fit more in.
Ask yourself: " Does this make sense? "
The answer is no.
There is always another natrual number.
You can’t "run out"
bait
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>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"-
>To be a banana is to be yellow. There is no larger "Yellow"
Incoherent babble
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just as
>To be infinite is to have no maximum. There is no larger "No maximum"-
Is there a maximum natrual number.
I only want a yes or no.
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No
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So there is "no maximum"? Right?
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maximum of what?
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Maximum number of times you will take the bait.
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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
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so?
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"So?"
Huh?
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how is that relevant to some infinities being larger than other infinities
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Because some infinites aren’t larger than other infinities otherwise they’re not really infinite.
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Lol. Then why can’t you map the reals onto the integers, you giant scrote?
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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.
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>I don’t have to map shit
Yes, you do. If we’re talking about identical amounts, there is a one-to-one mapping. -
>I don’t have to map shit
how else would you compare two amounts? -
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.
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>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? -
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.
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>You can’t "compare" infinites
Then why are you telling me all infinities are the same? -
Because something is the same as itself you scrotebrain.
Is 5 the same as 5? Are there 5s that are bigger than other 5s?
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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.
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Does how you "choose" to "map" infinites
Affect the results you get? -
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?
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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.
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>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"? -
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.
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>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? -
Yes
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So which one is it, scrote? Are they equal, or are they incomparable? These two positions are mutually exclusive by definition.
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I answer aftwr you answer my question
>Is a tower stacked with natural numbers "shorter" than a tower stacked with real numbers? One block for every element in the sets.
Answer
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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.
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>no
There you go.
I’m done here
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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.
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Yes, it’s shorter.
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Sounds like you’re every bit as scrotebrained as him.
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>I have no argument
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>comparing the sums of divergent series
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who is comparing sums of divergent series?
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scrotebrains talking about the heights of towers made up from infinite blocks.
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the heights are not well defined, but one can say that the real number tower is higher than the natural number tower
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>divergent series have no defined sums, but we can say that the sum of one divergent series is larger than the sum of another
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why are you still talking about divergent series?
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scrotebrains talking about the heights of towers made up from infinite blocks. You’re clearly mentally ill.
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I’ve told you. The heights are not well defined, but that doesn’t mean one cannot says that one tower is higher.
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>The heights are not well defined
Then what do your imaginary comparisons have to do with mathematics? -
Everything
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Mathematics doesn’t deal with things that are "not well defined". Sorry.
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That’s what I’ve said. The height is not well defined.
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>my infinite towers analogies have nothing to do with mathematics
Okay. Glad we have that settled. -
yes, it does. one tower is higher than the other.
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>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. -
no, one tower is higher than the other in a perfectly valid mathematical sense.
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>i’m a mouth-breathing imbecile
Yes, that’s exactly what I’m saying. Thanks. We can end this discussion here. -
why are you resorting to insults?
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Not an argument.
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>>i’m a mouth-breathing imbecile
>Yes, that’s exactly what I’m saying. Thanks. We can end this discussion here.
is an argument? -
Still not an argument. Sorry. Can you come up with a decent argument next time?
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I have plenty of arguments. it’s impossible to present them when you keep shoving words into my mouth though.
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Nope, that was still not an argument. I guess you just don’t want to have a courteous and civilized discussion.
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>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
:^) -
Was that an argument? I don’t think so. Too bad, I really wanted to have a civilized discussion with you.
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then why did you insult me without any reason?
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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.
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I am. just stop insulting me and shoving words into my mouth.
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That was not an argument, nonny.
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of course not. why should I give you any argument when you clearly don’t want to hear it?
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>why should I give you any argument
See? You’re not a rational or civilized person at all. -
>You’re a rational or civilized person
thank you 🙂 -
That’s not an argument, either.
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>That’s an argument
I don’t think it is, but thanks for finally agreeing with me -
Nope. Still not an argument.
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>Yes. Still an argument.
stop it, you’ve already acknowledged that you were wrong -
>i’ve already acknowledged that i breathe through my mouth
ok -
>ok
thanks -
do you compare numbers by the fact that you can run out? 4=5 because both run out?
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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.
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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’
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That’s nice, but how do I know they’re equal using your "running out" system, scrotelord?
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>. 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? -
>I’m gonna pretend the quantification is universal instead of existential to derive contradiction
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infinity is an amount
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prove it
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100
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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?
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Real numbers were a mistake, take the wildberger pill.
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woke af
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[…]
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""".-
npc’s fingers wrote this.
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>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.
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>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
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woke af
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holy fuck this dude just ended
There is ALWAYS space left over in bag that has no maximum of how much it can hold. You can always fit more in.
entire argument and career while at it, do you not feel any shame after being exposed as a clown?
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[…]
[…]
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.
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seething
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I am the biggest one.
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The question wasn’t who the biggest scrote ITT is.
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>>Some infinities are bigger than other infinities
complete and utter schizophrenia.
Hitomi theory solves all of this. -
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woke af and Cantor-Schroder-Bernsteinpilled, also witnessed
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>all the screeching wildbergers itt
get a life fucktards -
>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"-
Are three infinities bigger than two infinities? What about infinite infinities?
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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.
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>the biggest infinity?
tRump’s lies -
Since a subset of an infinite set is infinite:
Let the subset be human consciousness:
therefore, freewill existsInfinite choice offers infinite chosen, even if the choice is predetermined
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The fifth one
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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.
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