“There are infinite numbers between 0 and 1. There's .1 and .12 and .112 and an infinite collection of others...

Green is shit and everything he writes is pure shit so that doesn't excuse the fact that it's shit because a teenage girl was supposed to say it because it's still fucking shit

it's wrong though
from a set theoretic perspective there are exactly as many numbers between 0 and 1 and 0 and 2
of course 0-2 has a bigger measure but it's dubious if that's a meaningful definition of how many numbers there are

Well, infinity is non quantifiable. Infinity+1 isn't a valid statement. So it's infinity and infinity and infinity. Look. I just know what I read. I also read that a coffee mug and a donut have the same base shape. I was 12. All I can tell is what I read, and that John Green isn't pulling it out of his ass. You can rag on him for whatever, but not for that.

When Green is this far up his own ass with pseudointellectual bullshit ""prose"" I don't think writing in character is still a valid excuse.

you are wrong that infinity isn't quantifiable though
the aleph (cardinal) numbers count infinity and there are exactly as many numbers (technical word is that they have the same cardinality) between 0-1 and 0-2, aleph-1 in both cases

and coffee mugs and donuts are homeomorphic to each other, meaning they're topologically equivalent (meaning they share a lot of the same mathematical properties) but of course geometrically very different

>there are infinite numbers between 0 and 1
do normies seriously not realize this in like middle school?

Alright, I concede, you sound like you know a lot more about it than I do.

It's not good and it's not even right, at all. There are no bigger and smaller infinites. The number of possibilities between 0 and 1 is the same as with 0 and 2 or 0 and 1000000. It's infinite.

graduating with a degree in math this spring

set theory and the cardinality of infinities is pretty simple though and even youtube videos can give you an adequate understanding (for example just the numberphile video youtube.com/watch?v=elvOZm0d4H0 or vihart youtube.com/watch?v=23I5GS4JiDg ) unlike say the donut-mug thing whose idea is simple enough (the rubber analogy) but whose relevance relies on some understanding of topology which is far beyond the scope of such a video

Yes there are. Now Green is wrong about which infinities are bigger than others, but it's true that some are. Cantor proved it. There are more real numbers than there are natural numbers, but an infinite number of each.

Everyone learns it in high school, you elitist pseud.

It's not really

t. Someone who read quantum physics books

Yeah. I'm pretty good at geometry, and abstract theories in general as long as there's a concrete goal to work towards. The flip side is that once it get's too abstract, I'm fucking lost.

But I mostly gave up when I realized I couldn't even visualize a concept beyond a certain scale.

I can understand basic quantum theories if someone explains them in simple terms, and I can even come to certain theories on my own, but visualizing a trillion? Fuck it. I figure, if I can't do that, there's no real point.

I'm a right brain type, so I leave math to the left brain types, and settle for only knowing idiot math.

Lol at all these pseudo intellectual retards ITT clamoring to make sense of the nonsense they have read over the years. There is more potential between 0-2 than there is 0-1, and that is the definition of infinite. Get off Veeky Forums and go post on pol, dumfucks

Why would you want to visualize a trillion?

But it's something one should realize naturally at some point after they learn about decimals and fractions, it only makes sense.
You aren't actually telling me you had to be told this are you?

neat b8 m8

Why the fuck would you want to visualize that? You're doing it wrong.

Infinity + 1 is well defined as long as you can make infinity well defined. Conway showed in 1969 we can do this by discovering surreal numbers. C.f. en.wikipedia.org/wiki/Surreal_number

I don't know. I used to watch a lot of astronomy shows, and they always talk in extremes. Extremely small and extremely huge. If they can talk in those terms, doesn't it mean people visualize those terms? I thought I just wasn't good enough. Do people not visualize their math? Is that... is that not a thing?

>people ITT acting like infinity is a number and not a concept

There are the same amount of numbers in (0,1) as there are in (0,2).
f: x --> 2x

>humanitard can't grasp a simple mathematical abstraction

>Do people not visualize their math?
Only if they are dividing spple's into groups. There comes a point where you can't really "visualize". How do you visualize more than 4 dimensions?

>left brain
>right brain
Christ I hope you don't mean this literally

I'm actually studying astronomy and nobody can visualize those kind of things. It doesn't work that way my dude. You either have bad professors or never really asked your doubts. What were you studying when you realized math wasn't for you?

see

It is a thing. This is the reason you have a math degree and those other guys don't.

Numbers aren't even real.

ITT: People who visualise math but want to pretend the sign of true genius is to not visualise, just how they claim they don't sub-vocalise when they read.

I visualized all the way up until we were doing chance math, but those long fractions (with placement letters) completely destroyed me. I couldn't even figure out what I was supposed to be doing. I thought I had dyslexia, but for math. I'm long out of school now, but that explains so much.

Oh, I wasn't studying at all. It was grade 12 or so. Up until then, I had 2s, then 3s. Grade 12 I had nothing but 6s. I studied design instead. I love design and art, but the dream is deep sea marine biology. That of course precludes math, so... I figure, when I have my mid-life crisis, I'll do night classes or something. Who knows.

Jesus christ you were but a kid man, what's wrong with you? And marine biology? Don't you realize the math required for that is really basic stuff?

this xD mathcucks btfo

Fuck it you have spare time if youre posting here user dont be lazy.

MIT OCW for decent structure on any topic you want to learn

feynmann lecture notes for the big topics in physics to get into them.

Then just download a textbook in a topic you want, download the answers to the questions in it online, work though that shit.

When youre smart youll thank me.

pure maths is stupid and dull learn phsyics but get all pre req maths out of the way

The same way that phi and litards complain about stemtards talking out their ass about things they don't have good knowledge of, I'm reminded that there's also the other side.

I guess I assumed I'd fail. I was really demoralized, because I saw a steady decrease in my grades, and it hurt. I was completely helpless, and no amount of explaining could fix it, so I abandoned the sciences all together. It could have been a compounding of my circumstances, and I'm not unhappy with my schooling choices- learning design was pretty amazing, and made me see the whole world differently, but, well. I haven't given up on my dreams either way.

Thanks user. I don't actually have much time, because I'm trying to settle into a job (theater set and costume work) It's just an internship right now, but who knows. Also, I'm trying to learn french on the side.

There are an infinite number of guys that may be fucking your wife at any moment John Green.

Aye, I know how it is to be short on time. I study phyics so i get to spend time reading into topics and that interest me and solving problems from textbooks. Everyone should get the chance to, uninterrupted it can be magical provided you have a decent textbook. Learnt French in school, currently going to Dutch classes now, want to read the big 4 post ww2 dutch writers among others, picking up a language in your spare time is a smart plan.

>wife (male)

On the topic of John Green, it bothers me so much that someone his age engages in the kind of stupid behavior celebrated by tumblr.
I mean, I understand why, but it bothers me anyway.

The rest of this retarded thread aside, this post is pretty funny and I'm glad I got the chance to witness it because it's truly emblematic of the posturing pseud infestation that has and always will afflict Veeky Forums. You need to be an absolute retard to confuse basic concepts in set theory with "quantum physics". And the fact that this poster found immediate recourse in "quantum physics" when tasked with attempting to explain something he didn't understand just goes to show how easily trends in popular science warp the everyday perceptions of impressionable young adults. Thanks again

But how old are you and why do you care so much about what your 12yo you thoughts were in that moment? Maybe you're still very young, like 20 or something, but believe me, what you thought at that moment is completely irrelevant. Also at that age I didn't give a fuck about grades and that sort of things. That's more of an adult concern. I started to do some serious studying when I was in uni and as the years went by, it grew nothing but more serious (I'm 31 by the way).
If you want to be a marine biologist, start studying. It really is that simple. You stop being an emo kid and learn what you gotta learn. Grow up my friend.

There are different sizes of infinity, but it's not that one infinity is 'bigger' than another the way numbers are. They're really more like different types of infinity. 0 to 1, and 0 to 2, is the same type of infinity, so they're the same 'size.' They both have infinite values between them.

An example of a different kind of infinity is the set of all whole numbers. 0, 1, 2, 3, ...

That's a 'smaller' infinity than 0 to 1, because there's no inbetween. Between any 2 values in the big infinity, there's an infinite number of values between them. While as when you're only counting whole numbers, there's always a finite set between two values.

That's what is meant by different infinites. It's actually very basic math, kids can learn this shit. John Green is a fucking idiot.

>being cucked by aristotle

Yeah, I enjoy language a lot.

I wasn't being emo- I was stating straight fact. There is a huge difference between those two things.

John Green is correct in the measure-theoretic sense. That's clearly what he meant, he's published numerous works in the field.

You don't even know what visualization is.

All objects in your perceptual field (imaginary or real) are groups of abstract but tightly interwoven concepts and contexts. If you can have a theoretical understanding of larger numbers and you can integrate that understanding into your library of concepts then you can visualize it.

To understand it conceptually is to visualize it. You may not hallucinate it like you do the computer you are typing on, but you know it all the same.

Don't let theatrical pop scientist meme you into thinking that the complexities of reality are unknowable. Most of them don't even know where the fuck they started from so they are hardly authorities on what can and cannot be understood.

You visualize a 5th dimension by understanding its rules on a conceptual level. We live every day of our lives in the 4th dimension so its easy to wrap our heads around it without effort. We spend no time thinking about higher dimensions, thus we aren't well practiced in seeing them. Perhaps we can never truly imagine in our mind like the pictures of 3 dimensions we see. But if we know all the rules by which they operate, why would we need to imagine them?

Doesn't he mean visualization as in "a physical exemplification that could describe by analogy what's meant in theory".
Sort of like, what is ten? and you put ten bananas.
I'm not sure I agree entirely with you... Visualization not as "understanding the concept" but more like being able to create a mental image which represents the thing, as per one of the definitons.
At some point the way I visualize certain subjects, which are so far into the abstract without a macrophysical analogue, is basically the numbers, symbols, and papers I've read or written about them.
I dislike using quantum physics to give examples but I guess it's ok here.
Picturing spin/flavour, wave-particle duality, wave function collapse, and all that... takes place as simply the way I would write it in a scientific paper (so, algebra).
I disagree with you in the sense that I can't visualize things in their raw form.
The same way I can't picture more colors even if I know there are frequencies beyond our visible color spectrum.

Also.
4D is NOT Spacetime. 4D has 4 dimensions with all the same geometric properties in euclidean space (or the defined space).
Spacetime is 3 dimensions with then time added as an extra dimension but it doesn't have the exact same properties.
4D can be visualized in the sense that 3D can be visualized in a 2D space (the way you can draw a cube on paper), but to visualize 5D cleanly you'd need a 4D space to picture it, and we only have at hand 3D space to then visualize 4D, so we project in a 2D space (video or paper) a 3D view of 4D which then would need to extend to 5D.
It gets less and less clear, and at some point there's a lot of missing information and the only way to "see it" is in raw numeric/algebraic form.
Whether we live in more dimensions than 3D+time is a matter of debate (physics, dunno in philosophy), but we certainly only perceive (afaik) 3D and time. Everything else (from our perspective) is a projection onto the 3D+t plane.