Which number is bigger?

how can one figure this out? nonmath pleb here

PEMDAS
or BODMAS if you're from a civilized country

Ideally you would find the "dominant" term of each sum (that gives the order of magnitude) and compare these for starters (in the same way that to compare two integers you start with the numbers of digits and the first digits).
The problem is that it's hard to estimate which term of each sum is the biggest

What's his point? Something something ultrafinitism?

That there are expressions that are literally impossible to turn into numbers.

If the result of tht expression is bigger than 10^10^200 then it is impossible to find what number it corresponds to.

He claims this is a problem.

the point is that this math involves concepts understood by any 10 yo , but you seem unable to answer the question.

Where [math]10^{10^{200}}[/math] is something-something plank units in the observable universe.

Such a silly argument. By that same token, if you think numbers are strokes on a whiteboard, the biggest number would be about 10,000,000 given the number of whiteboards in the observable universe.

Couldn't you theoretically write a decimal number on each plank volume to numerically represent a number much bigger than that?

Wildburger says numbers are strokes on a whiteboard. Ergo if numbers are limited by what can be written given the resources in the observable universe, the biggest number is 10,000,000.

>theoretically
nobody cares about your fantasies. either you do it or you admit you are impotent.

They already are numbers. And what we can practically simplify into decimals is of no consequence.

...

>They already are numbers.
But are they?

Wildburger says that mathematics should abide by the law of 'logical honesty'. He goes into detail on this in one of his video. The point is that you should not assume that you can do something you actually can't.

So, if you want to say that you can assume those expressions are numbers then you better show first that given any arbitrary expression you can easily construct the number it represents.

Can you?

I'll go easy on you. Give me the number that represents the bottom expression in the OP's pic and then I will believe that we can assume those expressions are numbers.

protip: You literally can't.

Now, if you think that the law of logical honesty is dumb as I do then you are free to do so but we can at least accept that Wildburger is a better person than us for trying to do mathematics while abiding by that law.

this has to be bait.
>using resources in observable universe
>pick up pencil and write a number
10000000000
>its over 10,000,000

>Wildburger says that mathematics should abide by the law of 'logical honesty'.
Non-mathfag here, isn't that constructive logic by another name? How does that fit into what the HoTT guys are doing?

That's shorthand, not the actual number. Wildburger says that numbers are physical strokes on a whiteboard.

For example, "8" or shorthand for: llllllll. If "llllllll" were written on a whiteboard, that would be the literal number 8.

that's a pretty smart definition tho

Yeah, no. It's completely and utterly terrible. What will we do when technology has made whiteboards obsolete? Arbitrarily redefine our foundations?

A physicalist basis for mathematics is never a basis for mathematics.

ok well we don't have large enough whiteboards, but I'll assume that we could use individual objects as 'strokes'.
You can go over 10,000,000 just by counting the grains of sand on a beach. or by counting the atoms in a cubic meter of water.

this desu fampai. that's like saying you cant do mathematics on the economy because it involves numbers too large to write with fucking tickmarks on a whiteboard.

>What will we do when technology has made whiteboards obsolete?

You missed Wildburger's point entirely. He made a video talking about the fundamental dichotomy of mathematics. You either have something or nothing.

2 = II = 2 somethings
0 = = nothing

Strokes on a whiteboard are simply one way of visualizing 'somethings' and 'nothings'.

It is very similar to the way ZFC defines numbers

0 = {} that has 0 elements.
1 = { {} } that has 1 element
2 = { {}, { {} } } that has 2 elements
3 = { {}, { {} }, { {}, { {} } } } that has 3 elements
...

Why do you complain about Wildburger's burger but not complain about ZFC when they are literally equivalent (in terms of the way they construct natural numbers)

he's probably complaining about wildburger and not zfc because you brought it up

they're both not good

>they're both not good

Well, I think both are good. And obviously Wildburger's way is better if he is somehow able to go beyond.

Seriously, if WIldburger takes this theory and evolves it until he creates 'Rational Analysis' the same way he created ' Rational Trigonometry' I am going to suck his dick and become his PhD student because that shit will bring mathematics to a whole new level.

His last video (published today) was talking about divisibility so he is getting close to defining rational numbers in his system.

>Wildburger says that mathematics should abide by the law of 'logical honesty'. He goes into detail on this in one of his video. The point is that you should not assume that you can do something you actually can't.
This is political rhetoric and not mathematical. I just said that we can't practically simplify such an expression into decimals. That has nothing to do with whether the expressions are numbers though.

>So, if you want to say that you can assume those expressions are numbers then you better show first that given any arbitrary expression you can easily construct the number it represents.
The expressions are finite series of well defined operations on numbers within the domain of those operations, so the result must be a number. This is not an assumption. If you want to say that this is not a number, then you better show how it could not be.

>I'll go easy on you. Give me the number that represents the bottom expression in the OP's pic and then I will believe that we can assume those expressions are numbers.
The number is already there written down on the board. You are asking me for the number in decimal form, not "the number". But why does the decimal form matter? It's arbitrary.

>Now, if you think that the law of logical honesty is dumb as I do then you are free to do so but we can at least accept that Wildburger is a better person than us for trying to do mathematics while abiding by that law.
Troll or retard?

So he's confusing an arbitrary representation for the number itself.

danks bros

>The expressions are finite series of well defined operations on numbers within the domain of those operations, so the result must be a number.

Freshman detected.

What you are saying about the defined operations on numbers is true but that only that proves that IF the result exists, it will be a number as you cannot possibly get out of the numbers by operating numbers.

If x = 2/0 then we know that x would be a number but it does not actually exist.

He is saying that this same thing happens to such large expressions.

You have proven that if the answer exists it must be a number. Nice job.

Can you prove that the answer exists?

In Wildburger's system he claims that there is a set of expressions and a set of numbers.

Your claim in his system boils down that saying that there exists a function from Expr to Nat so that for every element of Expr there is a matching element of Nat

What is this function? I don't know, he claims it does not exist.

But again, I will go easy on you. What number is that expression mapped to under this supposed function?

If you can't tell me then you cannot assume you could tell me. Law of logical honesty and shit.

>What you are saying about the defined operations on numbers is true but that only that proves that IF the result exists, it will be a number as you cannot possibly get out of the numbers by operating numbers.
No, if an operation is well defined and the numbers being operated on are within the domain of that operation, the result must be a number. Otherwise the operation is not well defined.

>If x = 2/0 then we know that x would be a number but it does not actually exist.
Division by 0 is not well defined. Either there is seriously something wrong with your brain or you are trolling. Just tell us which one it is.

>He is saying that this same thing happens to such large expressions.
They can't in this case. There is no division or subtraction, no way to get outside the domain of multiplication or addition. He chose his example badly. Except he doesn't think he chose it badly because the point he is making does not make sense.

>You have proven that if the answer exists it must be a number. Nice job.
No, I proved the answer exists.

>In Wildburger's system he claims that there is a set of expressions and a set of numbers.
No one cares. We're not doing math in his system, we're doing math in the standard system. If he wants to say the standard system is wrong he should prove it contains a contradiction, not fuck around in his own system.

>Your claim in his system boils down that saying that there exists a function from Expr to Nat so that for every element of Expr there is a matching element of Nat
>What number is that expression mapped to under this supposed function?
You clearly don't understand what a number or function is. The expression is already a natural number. The function that maps it to a natural number is the identity function.

>The expression is already a natural number

Well, what is this natural number? Where is it?

What is the first digit?
What is the last digit?

>You clearly don't understand what a number or function is.

Look, in his system Expr is a set and Nat is a set. You claim that there exists a surjection from Expr to Nat.

If this surjection exists then at the very least tell me what it maps the expression in OP's pic to.

>The function that maps it to a natural number is the identity function.

Okay then. Now can you tell me what the number is?

You know, you think I am trolling but I am actually answering you in the way he would answer. If you were to go to his channel and post a comment asking him about this shit he would tell you exactly this. What is the number that corresponds to that expression?

You are clearly not understanding the point of what Wildberger is doing. If the theory of arithmethic is so perfect and well defined then why can't you not tell me what is the natural number that comes out of that expression, written as an element of Nat.

Just to remind you, elements of nat look like [IIIII]

But I will go even easier on you. Tell me what does this number look like as an element of Num (our usual decimal system).

Go on, tell me. Write it down.

π.

>Well, what is this natural number? Where is it?
It's right there on the board retard.

>What is the first digit?
>What is the last digit?
I don't know, nor do I care. Again, your fixation on the decimal form of the number is arbitrary.

>Look, in his system
bzzzzzzzzzzt, wrong. Try again.

>Okay then. Now can you tell me what the number is?
It's written on the board. Can't you read?

>You know, you think I am trolling but I am actually answering you in the way he would answer. If you were to go to his channel and post a comment asking him about this shit he would tell you exactly this.
Yes, and he's a retard.

>You are clearly not understanding the point of what Wildberger is doing.
I understand it completely.

>If the theory of arithmethic is so perfect and well defined then why can't you not tell me what is the natural number that comes out of that expression, written as an element of Nat.
First of all, the expression is already written as an element of the natural numbers. You are confusing decimal form with the number itself. Which is flat out retarded.

Second of all, the impracticality of writing the number in decimal form is mathematically meaningless. It does not show a problem in arithmetic any more than your inability to orbit the sun a billion times represents a flaw in rocket science.

>Just to remind you, elements of nat look like [IIIII]
Wrong.

>Tell me what does this number look like as an element of Num (our usual decimal system).
As it looks like on the board. Stop asking question I have already answered.

2 = 1 + 1 = 2-1 = 2*(2^0) = 2^0 + 2^0 = [II] = { {} , { { } } }

If you don't find meaning in wanting to define these equalities then you are not fit to be a mathematician.

I have nothing else to say. If you want to see a different perspective then just watch his videos directly and see what he is trying to do.

>If you don't find meaning in wanting to define these equalities then you are not fit to be a mathematician.
Non-sequitur.

>I have nothing else to say.
Yes, you have no answer because you have no point to make. I hope you learned something today.

>Non-sequitur.

If a mathematician is someone who asks new questions about mathematics and you are trying as hard as you can to not ask questions then you are not going to be a mathematician.

His is a foundation of mathematics that assumes less about ZFC. One of the most notable characteristics is that it does not assume infinite sets exists, among many other things.

You do not understand meta mathematics. If this were the 19th century you would be categorically a retard. The only reason you can so comfortably accept the statements you accept is because a foundation for mathematics is already established, namely ZFC.

Back then if you were to undermine the efforts of the mathematicians figuring out what axioms were fit to be our foundation then you would be the biggest moron of the town.

>If a mathematician is someone who asks new questions about mathematics and you are trying as hard as you can to not ask questions then you are not going to be a mathematician.
You don't understand. That implication came out of nowhere. I'm not even going to address it because it has no connection to anything being said. That's it.

>His is a foundation of mathematics that assumes less about ZFC. One of the most notable characteristics is that it does not assume infinite sets exists, among many other things.
There are many foundations that do this. Wildburger is not making a serious attempt at ultrafinitist mathematics. He seems more interested in spreading political rhetoric and pretending that he is not using axioms. It's a joke and I'm not spending any more time discussing it. You are a fool and this discussion proves it. I'm out.

>shut up and calculate! symbols mean nothing!

>Given [math]\left( m,\, n \right) \,\in\, \mathbf N[/math], [math]m \,+\, n[/math], [math]m \,\times\, n[/math] and [math]m^n[/math] are all natural numbers since + and × are both closed in [math]\mathbf N[/math]
>[math]8^{8^{9^{7^{3^{5^{11^{10}}}}}}} \,+\, 19^{37^{45^{3^{4^{7^{8^{15}}}}}}} \,+\, 1375 \,\times\, 578^{1032^{5^{4^{7^8}}}}[/math] is not a natural number
(You)

Nice argument. Now please write that number down.

No, you know, that could be too hard. Just write down what the last and first digits are and a short proof showing that those numbers are indeed correct.

I know you can do it, should be easy. I mean, you claim it is a number so all you have to do is look it up and type down two digits.

(You) (You) (You) (You) (You) (You) (You) (You) (You) (You) (You) (You) (You)
>A number is a sequence of digits
Go back to primary school LMAO.

Just accept that you can't.

Wildberger accepted that he can't and now he is trying to rebuild arithmethic in a way that avoids these holes, as he would call them.

Stop being faggots.

brainlets do not know that they cannot count beyond 10^200 with the usual arithmetic

In my opinion, the ultrafinitists are evil!

Long live transfinite set theory!

>he fell for cantor's diagonal argument

That's not an argument.

All of those are reals on the board though

All he’s done so far is adding artificial holes by saying “cant du dat not rigoroose”. Come and see me when his axiomatic accomplishes *anything* the mainstream one has yet to do.

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
I can even write it down so that you know it’s a number. :^)

Go read Kant's Critique of Pure Reason and learn the difference between abstract objects and schema you idiots.

This autism is the result of trying to do logic without a strong philosophical framework backing it.

Why doesn't closure apply?

Hint: [spoiler]it does[/spoiler]

>no one is able to actually answer wildberger's question

infinitists BTFO!!

so, what happens if we use a 60-digit system like in Babylonia? does that mean the universe is then larger? how many digits can we use? what if we use a 10^200 digit system?

>1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

>???

Given that Wildberger arithmethic is defined over msets, you could certainly construct arbitrarily big numbers by they mean nothing because they cannot work as numbers.

Makes no fucking sense.

So what's Wildburger's opinion of, say, set theory? It's obviously valid mathematics as every proof is equivalent to a formal Hilbert-style proof from a finite number of axioms. Does he just find it valid but meaningless? Seems like mere personal taste.

the reason they shouldnt mean anything is because nothing in the universe can support a number that big, not because
>muh cant work

What the fuck is he trying to say?

>Can't even afford a proper whiteboard
How am I supposed to take this guy seriously?

I bet he finds it not rigorous because muh infinite amount of work.

Just another Planck distance meme.

What are you talking about? A formal proof is just a string of formal sentences each of which is either one of the finitely many axioms utilized in the proof, or filled from a prior by modus ponens or propositional tautology. That's what a formal proof is in any discipline of mathematics. Finite and algorithmically verifiable.

what holes? that we can't represent a number in a particular way doesn't mean that number doesn't exist or is not well defined

Yes but according to Wildburger it takes an infinite amount of work to make sure things like induction applies and that therefore it’s not rigorous. Just a retard way of tricking yourself into believing every proof containing [math]\forall x \,\in\, S[/math] with [math]S[/math] infinite is unrigorous.

How does he know the size of the universe though? We only know the size of the observable universe

Yes, that is retarded. Any instance of the induction schema is just a single sentence. From a proof-theoretic standpoint, all reasoning in any discipline of math is finitary.

>mfw wildburger threads are going to cross over with Problem of Induction threads
im excite

Someone tell this guy you're allowed to express understanding of a concept and discuss its implications without necessarily agreeing with it, because he's fucking the whole thread up.

Well in his defense, he's completely right, and it was a relief to finally see the obvious being said.

This question is invalid because it assumes existence of numbers greater than [eqn]10^{200}[/eqn]

8^8^9^7^3^5^11^10
< 8^8^9^(6^2)^3^5^11^10
= 8^8^9^6^(2 * 3^5^11^10)
< 8^8^9^6^6^5^11^10
< 19^37^9^6^9^6^152^14

19^37^45^3^4^7^8^15
< 19^37^(17^2)^3^4^7^8^15
= 19^37^17^(2 * 3^4^7^8^15)
< 19^37^17^6^4^7^8^15
< 19^37^17^6^4^(6^2)^8^15
= 19^37^17^6^4^6^(2 * 8^15)
< 19^37^17^6^4^6^(8 * 8^15)
= 19^37^17^6^4^6^8^16
= 19^37^17^6^4^6^8^(2 * 8)
= 19^37^17^6^4^6^64^8
< 19^37^17^6^9^6^154^14

1375 * 578^1032^5^4^7^8
< 578^(2 + 1032^5^4^7^8)
< 578^1033^5^4^7^8
< (19^3)^1033^5^4^7^8
= 19^(3 * 1033^5^4^7^8)
< 19^3099^5^4^7^8
< 19^(10^4)^5^4^7^8
= 19^10^(4 * 5^4^7^8)
< 19^10^4^5^4^7^8
< 19^10^4^5^4^(6^2)^8
= 19^10^4^5^4^6^16
< 19^37^17^6^9^6^152^14

8^8^9^7^3^5^11^10 + 19^37^45^3^4^7^8^15 + 1375 * 578^1032^5^4^7^8
< 3 * 19^37^17^6^9^6^152^14
< 57^37^17^6^9^6^152^14
< (23^2)^37^17^6^9^6^152^14
= 23^(2 * 37^17^6^9^6^152^14)
< 23^74^17^6^9^6^152^14
< 23^104^17^6^9^6^152^14
< 17^35^42^10^6^3^10^11 + 23^104^17^6^9^6^152^14 + 791 * (10^10^10^10^10 + 39^39^39^47^2^18)

>there are 10^200 Planck cubes in the universe

There are about that many in the current observable universe, but that number increases over time. Also making claims about the unobserved universe is pure conjecture.

>at best we can fill each with a digit 0, ... , 9.

At best we could fill each with a digit 0, ... , n of arbitrary value. Trivially, # could represent n-1 in base n.

Should I start my own channel, guys? I think I just revolutionized rational mathematics.

...

They aren't wrong, though.

The reasoning was invalid. She had a 50% chance of getting it right, and she did.

particularly
>That last term settles it.
The third term is by far the smallest term in both expressions.

>she
Where is that coming from?

Please don't comment on the pronouns. This thread is about the math, not the pronouns.

not him/her, but the only sensible answer to your question is that that person is a woman too. just as men refer to other anonymous posters with "he", women use "she", you filthy pig.

>at best we can fill each with a digit 0,1..9
what about a numeral system with more than ten digits, though

what if my digit system had 1000 different distinct single-digit characters each representing a single distinct number

Ok... it is just that I am the person who posted I am manly man's man.

>makes a comment pretending they want to redirect the topic from a less relevant subject (the pronouns) to a more relevant one (the math), but in reality they're more interested in the followup inquiry by curious posters who want to speak to a girl browsing Veeky Forums.

Why would someone do this? Why would a person go through all that effort.

The answer is: you're a pseudo-intellectual elitist whore mongrel that knows nothing of math but desperately wants attention from pathetic autists on the internet.

Kill yourself, you pathetic ugly whore.

>curious posters who want to speak to a girl browsing Veeky Forums.

If there is anyone who is actually characterized by this sentence then I feel sad for them. We've found the cuckiest cucking cucker cucks in the universe.

user, I hope you are not projecting here because then you need to go into cuck rehab.

If all the integers on the board were 10, the answer would still be the same. You could cancel out the first two terms in that case, and the third term would settle it.

Except this is Veeky Forums and everyone is a white male by default.Claiming you are anything else without extremely good reason is attention whoring

Whether or not these "curious posters" actually exist is irrelevant. The female poster just assumed that there would be curious posters who'd poke and prod, questioning whether she was in fact a "she" - all the while her ego's in the stratosphere as she interprets this autistic behavior as flirtation.

>If all the integers on the board were 10, the answer would still be the same.
That happens to be true, but if you changed the 14 in the second term on the bottom to a 6 or lower, the answer would be different. The third term is irrelevant.

Look, I appreciate it when people shit and insult women on the internet because honestly it is hilarious but you went all out for no reason.

I can't really get into the feel of beating down women unless it feels like the person deserves it. I don't think she was doing anything wrong.

You shouldn't say that everyone is a white male by default. You should simply say that no one should even talk about race or gender.

When it comes to pronouns I guess there is an issue but I think we can all agree on saying he.all the time because we will be right most of the time while if we said she all of the time then we would be wrong most of the time.

The reason I got alarmed is that when someone called me 'she' is because I thought they were trying to make fun of me or something.

Wrong. We're all little girls. Get out.

>You shouldn't say that everyone is a white male by default
I should have been more specific. Unless you actively state otherwise, everyone here is a white male american. The only exception is a the odd board that assumes you are a white american female

>The only exception is a the odd board that assumes you are a white american female

/a/ does not assume that people are girls. The board about cosplay is the female board man.

Do you have sources for this shit? When I go to /a/ it stinks of semen.

I wasnt referring to /a/, the word "a" was a typo. I was referring to /cgl/ and any other board that is predominantly female if there is one