Thoughts on him?

Thoughts on him?

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en.wikipedia.org/wiki/False_dilemma
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Retard who still doesn't get infinity.

He has good arguement a against it desu

I haven't heard a single good one yet

I have nothing against infinity, however a good argument is about how we can't grasp such a concept intuitively and therefore we can only manipulate any "infinite thing" formally, as if we were using a very long tool that plunges into a world we can't see or understand that much. We are blind to infinity, but that doesn't mean it isn't a valid, useful or insightful concept. But you need to have faith, faith that what you are creating in the inaccessible world of the transfinite really does mean something and is not only mental masturbation via formalism. And it's not everyone who has that faith, and that's an interesting thing to me.

So what about an `infinite set'? Well, to begin with, you should say precisely what the term means. Okay, if you don't, at least someone should. Putting an adjective in front of a noun does not in itself make a mathematical concept. Cantor declared that an `infinite set' is a set which is not finite. Surely that is unsatisfactory, as Cantor no doubt suspected himself. It's like declaring that an `all-seeing Leprechaun' is a Leprechaun which can see everything. Or an `unstoppable mouse' is a mouse which cannot be stopped. These grammatical constructions do not create concepts, except perhaps in a literary or poetic sense. It is not clear that there are any sets that are not finite, just as it is not clear that there are any Leprechauns which can see everything, or that there are mice that cannot be stopped. Certainly in science there is no reason to suppose that `infinite sets' exist. Are there an infinite number of quarks or electrons in the universe? If physicists had to hazard a guess, I am confident the majority would say: No. But even if there were an infinite number of electrons, it is unreasonable to suppose that you can get an infinite number of them all together as a single `data object'.

I do not see how "a set which is not finite" is not a sufficient declaration, it is easy to grasp and makes just as much sense as the unstoppable mouse if you define stoppable, the leprechaun makes no sense tho. Also sets in themselves do not exist in the real world, just as much as numbers, but they still have use. It doesn't even matter if there is something inifinite in the universe or beyond that, the concept can still have merit.

Ironicly enough, using infinity gives a far better intuition for things than ugly discrete manipulations, you are right in that a lot of work around it could be mental masturbation like number theory has mostly been for the past 2000 years, but we have already seen aspects of this which were of use, so it's worth keeping. Unless infinity leads to logical contradictions, which it does not do according to current knowledge, there is no real issue here.


Anyone else got a better argument?

I know this is pasta but here's a (You).
An "infinite set" X is precisely a set that possesses a subset A, of which each element can be put into a one-to-one correspondence with each element of X.

>using infinity gives a far better intuition for things than ugly discrete manipulations
Please give me an example of this supposed fact.
>we have already seen aspects of this which were of use, so it's worth keeping
I agree with you. However most proponents of finitism and other similar schools of thought do not deny that infinite sets and the infinite in general are useful.

1) I agree with him on the absurdity of the infinite
2) I love his videos and watch many of them
3) happily taking his algebraic calculus course
4) he is not consistent in applying his own standards to himself

(4) is pretty minor since this is, as far as I can tell, part of the human condition, and anyway his own faults in that regard do not invalidate his reasons for disliking infinity bullshit.

Euler of our times.

quick question, if infinity doesn't exist, then whats the largest integer?

and if the integers are infinite, then aren't we still justified in saying that the reals are larger via cantors diagonal argument

The largest number is that which can be stored on a hard drive the size of the observable universe, writing data at the smallest physical scale. Any numbers outside this range are deemed dark numbers.

math doesnt bow the knee to physics

Oh! And what is it?

Sorry sweetie, without physics mathematics would have been lost to the history books.

go watch his fucking videos and learn for yourself, idiot.

I did, and all I heard was hand-wavy closet conspiracy nonsense.

Who is he????

coming from a classical indoctrination into mathematics, his ideas sound like drivel. unfortunately you need a very high IQ to understand and appreciate Professor Wildberger's arguments.

savior of mathematics

His videos are amazing

I most agree with him about infinite groups.

They are a total spook and are missing a lot of important properties.

what is money

He doesn't know. The point is that you can't make arguments that rely on using arbitrary large numbers that approach infinity as in a limit

> professor says "The infinite group of real numbers under addition"

Thats when you drop the class

>Professor Wildberger's arguments
That numbers are sequences of digits? Primary schoolers think that, and that's exactly the point of people who laugh at this senile retard's face.

>you can't make arguments that rely on using arbitrary large numbers that approach infinity as in a limit
but why tho

what issue is their with asking "how many rationals are their inbetween 0 and 1?"

>> professor says "The infinite group of real numbers under addition"
If they were finite then they wouldnt be closed under addition

all math is counting money now is it? LMAO

just a regular schizophrenic displaying early symptoms

hear whatever you want to hear. addition and subtraction would never go away, calculus would naturally arise in optimization problems but just keep crying about how great physics is.

who even cares if it would be forgotten, at least math is more consistent than phys

Doesn't answer my question.
"berger mathematician" finds several.

>quick question, if infinity doesn't exist, then whats the largest integer?
There's no reason to suppose an answer to this exists if you are willing to take ultrafinitism seriously. And it is not sufficient to even accept usual notation of numbers or operators since all of mathematical logic is built on unary notation (i.e. the successor operation) and not (say) decimal or binary. And indeed even writing something like [math]2^2000[/math] which is something a person could write down in binary (a 1 followed by two thousand zeroes is not inconceivable) but the symbolic explosion implied by this undefined shorthand is too impractical to be contemplated and any purported proof involving such a number could never actually be written down.

>If they were finite then they wouldnt be closed under addition
you can preserve closure in a certain sense—the exact details escape me—by introducing to your logic symbols which have the intended interpretation of "indefinitely large." The details were in the book "Understanding the Infinite" by Lavine. Quite a good read by someone who, while not a finitist of any sort, takes the notion seriously.

No one gets infinity, because infinity is a nebulous concept. It's defined by what it's not, without any a priori reason to think things can have that quality.

So we introduce an ambiguous concept of infinity just so our poorly defined number system can form a group? The fuck?

>It's defined by what it's not
Wrong.

>infinity fags accept infinity when they can't even work with FINITE big numbers such as Ackermann(4,3)
hohohohoho hahahahHAHAHAHAAHAHAHAHAHAAHAHAHAAHAAAHAHAHAHAHAHAAHAHAHAHAHAHA HAAHAHAHAHAHAAHAHAAHAHAHAHA

>>infinity fags
Why the apeirophobia?

it isnt ambiguous, it is the statement that "the sum of any two integers is another integer" if the integers were finite this wouldn't be true. There would be a largest integer and adding 1 to it would make the sum no longer an integer... because of that we say that the integers are infinite

Can't fear what doesn't exist.

>Can't fear what doesn't exist.
What about all the people with a fear of ghosts or the fear of God?

>conflating spiritual/theological argumentation with philosophic/mathematical argumentation
get your paradigms straight, before I call you a brainlet.

>>conflating spiritual/theological argumentation with philosophic/mathematical argumentation
Who are you quoting?

it was a joke maybe calm the religious defense team down a tad

9461027

Mark of a true brainlet, is those which cannot entertain a theological discussion without going full fedora.

its not a theological discussion asshat, it was an offhand comment. keep your fucking autism in check like the rest of us, shit

Wrong, it was a useless waste of data and should have never even been conceived to be posted in the first place. You want offhand comments go back to whatever shithole subreddit from whence you came

An idiot that knows too much to realize he's an idiot but not enough to not be one

>it was a useless waste of data
>theological discussion
pick one

and stop making mountains of molehills

this is a math thread, dont fucking reply to non math comments you unbelievable ass. If you want to screech about theology do it off of a fucking science board

I've made half the posts in this thread, jog on.

makes sense, half the posts here are just mindless complaints about infinity

>adding 1 to it would make the sum no longer an integer
you wouldn't be able to add 1 to it, so it would be the last integer, which doesn't invalidate the statement that any time you add 1 to an integer you get an integer

...so you claim there is an integer on which succession doesnt work, id like to see a proof of the existence of such a number.

It's quite simple to prove to yourself. Take 0. Apply successor. See how far you get.

>See how far you get.
you assume the existence of a final integer to prove the existence of a final integer

I don't know much about him but I have had similar thoughts ever since I learned about set theory. I am tried to create my own intuitions, and don't see how I could prove them or how another set could be better. I plan on reading Cantor myself.

>prove I can't add 1 forever or else I can
you sure will feel silly on your deathbed

the law of the excluded middle

either true or false, this is mathematical logic 101

claiming that the integers are finite requires proof, we have a proof of the infinitude of the integers but you dont assume that a + 1 is defined for every a, so math is apparently different for you

>we have a proof of the infinitude of the integers
...assuming infinite naturals, lol, back to mathematical logic 101 kid you're out of your league

>...assuming infinite naturals
where the fuck did i assume that, tell me

if you accept the PROOF of the infinitude of primes you must accept the infinitude of the naturals

the successor function is injective from the Peano axioms, and no natural has 0 as its successor. Theres the bare bones of a proof.

If you want to fight the Peano axioms go right fucking ahead, but then youd be playing bowling against a team of baseball players while screaming the whole time "you arent following the rules!"

either trolling or legitimately new to this topic and I don't care which

>either trolling or legitimately new to this topic and I don't care which
en.wikipedia.org/wiki/False_dilemma

A false dilemma is a type of informal fallacy in which something is falsely claimed to be an "either/or" situation, when in fact there is at least one additional option.[1]

A false dilemma can arise intentionally, when a fallacy is used in an attempt to force a choice or outcome. The opposite of this fallacy is false compromise.

The false dilemma fallacy can also arise simply by accidental omission of additional options rather than by deliberate deception. For example "Stacey spoke out against capitalism, therefore she must be a communist" (she may be neither). "Roger opposed an atheist argument against Christianity, so he must be a Christian" (When it's assumed the opposition by itself means he's a Christian). Roger might be an atheist who disagrees with the logic of some particular argument against Christianity. Additionally, it can be the result of habitual tendency, whatever the cause, to view the world with limited sets of options.

Some philosophers and scholars believe that "unless a distinction can be made rigorous and precise it isn't really a distinction".[2] An exception is analytic philosopher John Searle, who called it an incorrect assumption that produces false dichotomies.[3] Searle insists that "it is a condition of the adequacy of a precise theory of an indeterminate phenomenon that it should precisely characterize that phenomenon as indeterminate; and a distinction is no less a distinction for allowing for a family of related, marginal, diverging cases."[3] Similarly, when two options are presented, they often are, although not always, two extreme points on some spectrum of possibilities; this may lend credence to the larger argument by giving the impression that the options are mutually exclusive of each other, even though they need not be.[4] Furthermore, the options in false dichotomies typically are presented as...

Why not post the Peano axioms instead to "prove" me wrong?

>Why not post the Peano axioms instead to "prove" me wrong?
Because you presented a false dillema (a logical fallacy).

Or because you looked it up after showing your ass.

>Or because you looked it up after showing your ass.
What do you mean?

>A false dilemma is a type of informal fallacy in which something is falsely claimed to be an "either/or" situation, when in fact there is at least one additional option.

This is fucking math, the laws of logic apply since this isnt a fucking political debate

en.wikipedia.org/wiki/Law_of_excluded_middle

Any mathematical statement is either true or false, it is fucking impossible for it to be anything else.

Even if you enact incompleteness, any statement is still only just true or false, its just unprovably so.

See the criticism section on that wiki article dumbass

>This is fucking math
Do you need to swear?