Can programmers do math? What is a real number, really? 

Currently getting started on my math undergrad, guess i'll have to watch this video to know the ways of abstract tomfoolery.

A function is just a morphism in the category of topological spaces, so all functions are actually continuous

It gets worse than this: it's not possible for any real number representation to represent non computable numbers, so any "real number type" necessarily will have gaps you just cannot represent. That's why if I want rigour I will use an integer, rational or other algebraic type and otherwise... "floats are fiiiiine 😅"

My freshman year of college, I presented on p-adic numbers, and at the start I asked if anyone knew how real numbers are defined, which no one did. Literally everyone was operating on the "real numbers are the numbers in between the rational numbers" level instead of thinking of them as sums of smaller and smaller rational numbers. So I totally believe you that other disciplines never learn this 😂

Even though we don't know whether or not pi contains every possible string, I'd expect us to have checked relatively small strings longer than phone numbers and social security numbers, so the clip shown might be technically correct even though misleading.

As a meandering philosopher, Ultrafinitism is infinitely fun to drop in a math department with whilst armed with delicious controversy popcorn. I like to quip that a good lower bound is the value of the Ackerman function for the number of particles in the observable universe. Great video, thanks for making and sharing it.

can you make a video on the law of the excluded middle? It's really entertaining to see your jokes about it so please throw us more of it

The recording noise somehow carries subtle meaning and helps convey the flow of the video, well done!

One of the best video I've seen on youtube in my life

oh no. the level of nuanced shade was an immediate subscribe. Wow, this is brilliantly hilairous.

I have never met a programer who new anything about math let alone passed a math class. I understand that some degrees required a basic math background to graduate. But not the basement coders and self served programers and hackers. Known as geeks! I say let them wait..

Wow! This video is amazing! I've been thinking about this sort of issue for a while. Thank you! Have you seen any of Norman J. Wildberger (Mathematician) videos?

Nice video!

Wow you guys are smart I just like this because it makes me feel like a genius

I wonder if I could implement the unsigned integers in the same way that mathematicians do it: 0 = the empty array [], 1 = [0], 2 = [0,1], 3 = [0,1,2], for some n, n+1 = [all the elements of n, n], and we can keep going to implement integers, rationals, reals, and complex numbers.

I have a degree in applied physics, and I am a software developer with 6 years of experience and it's true, I have no idea how to do math

Давай!!! ДАВАААЙ УРАА ДАВААЙ ДАВААААЙ

I believe your representation of real numbers by Cauchy successions falls off when considering the distance between x and xn is less than 1/2^n. Mathematically of course it holds since the interval of a_n and b_n halves in distance each iteration; yet the algorithm implementation of such proof (5:31) loses precision when computing *rational mid*, since by dividing by 2 a binary number you are subsequently adding another bit. Now, I don't know how you implemented the *rational* class and if you've overloaded the / operator, but as long as it has finite bit representation, we've got a contradiction. The only silver lining is if *rational* would have size arbitrarily large depending on n, which would indeed be a crazy mad idea: Since you have perfect bit representation for any element in the set A made of 1,2, and the property (x+y)/2€A, with the fact that A is dense in R, we get the assurance that any real number on (1,2) can be the point of convergence of some succession of A (finally proving |x-xn|

This is the dual of the last video

As a computer programmer: most of us can't do math. I would point you to the Linux tool bc, though. It stores numbers in a manner such that .1+.2=.3 correctly, exactly, and with no magic. It is just slow (the version on Android is faster that the GNU version). As for me: if I say arbitrary precision, I mean an a priori precision, so that I can compute the working precision necessary for the final result to have that precision. And then the program would run at a fixed precision.

As someone taking their second semester real analysis class i never considered this application but its straight out of the textbook in theory lol

"why do programmers settle for the wacky artefacts of floating-point arithmetic?" I mean you could try asking them. And, hey, just because you're unable to explain a Monad to anyone that isn't a mathematician. It's ok. I still choose to believe that it's *not* just something math people made up to sound impressive.

Short answer: no.

Can you elaborate on how it's impossible to construct a discontinuous function ℝ→ℝ? Maybe I'm misunderstanding, but wouldn't something like f(x) = { 0 if x < 0, 1 if x ≥ 0 } be ℝ→ℝ and have a discontinuity?

congrats on 315 subscribers

I'm a computer scientist, doing math and physics and math pedantry is just not as fun as CS pedantry but we are at least lazy where it matters. When it feels good physics is not LAZY, it's GAMBLING

Ironically doing precise math is harder on high level languages then on low level ones. Probably doesn't fit with the video, but it's ok, i have still to watch it ;-)

I'm currently studying abroad in math. I can confirm that mathematicians are in fact this insane.

this channel is clearly very good but i did not ever really learn math so i have no way of knowing what youre actually saying half the time. is this different from bigint libraries in some way?

Does this mean that you can't check if a value is equal to 0? Or am I misunderstanding.

3:10 you forgot to assume a flat earth! 😱

JapanEat's alt channel

You aren't saying that programmers can't do math. You are saying that computers can't do math.

The information you're sharing is too important to have audio this bad. Where do I sign up to help fund better audio?

Programming has nothing to do with implementing mathematical abstraction. Never. The most it comes in the vicinity of that goal is to implement real world applications of those abstract concepts. And in this, programmer can become really good and useful. Most abstract concepts of mathematicians are completely decoupled from real world applications. Without those programmers, they would seldomly become useful for real life, and mathematicians would barely be as respected and useful as they are nowadays. As a mathematician, avoid going into disrespect against the most useful group of professionals that are out there to make your work into actually useful tools!

This has no connectin to real numbers

A real number is any value that does not contain i In the forms,xi, x+yi, and its negatives

Sorry, but I gotta say it for the meme: Have you considered rewriting this video in Rust?

Juste pour être bien sûr, t'es québécois ???????

Forget the logic, we have breaks and continue Who cares about speed of algorithms

i don’t know how to do math :)

My eyes grow dim waiting for the Lord the number of my enemies is greater than the hairs on my head people speak against me in the gate Lord i call upon thee in my time of trouble psalm sixty nine the Lord said to moses bring joshua to elisha the priest and in the sight of elisha commision joshua so moses found joshua and commisioned him Numbers you are of the flesh so i feed you milk because you are an infant not ready for solid food that is why you are jealous because you are of the flesh one corinthians

LEM bad

nerd

You've just proven that real numbers aren't real. They are an idea that is only formed by looking at rational numbers in decimal notation and saying "Wow, this notation is great, but let's make the amount of digits we can put after the dot unbounded". The moment you make any idea unbounded it ceases to exist in reality. Also, certain kinds of mathematical questions don't have actual answers. They only have rational approximations for answers that don't really answer the question. Like the question: "How many radi of a circle fit into it's circumference?". Your point on the ability to represent pi in a finite way using an integral over the root of 1 - x^2 is wrong. An integral isn't a finite process. It deals with adding infinitesimals together, which is yet another unbounded process. You can only calculate a Riemann approximatiom for it. Or, if you're lucky, you can get an antiderivative, which, when evaluated, can only be evaluated to a rational approximation. The second formula you mention requires you to select a finite number of terms to calculate an answer, which results in another rational approximation of pi. The number pi doesn't exist. All that exists are a bounded (not unbounded) number of approximations that we could feasibly reproduce for different use cases. Now, this doesn't mean that real numbers don't have any utility. They absolutely do in the conceptual/unevaluated domain (in question form). We can work in this conceptual domain until we've come to some representation which represents our question in the simplest way possible and the pull that into the real world by getting a rational approximation to it's answer at the very end. For the astute amongst you, you might realise that even rational numbers don't truly exist given that a ratio is just a question asking "What is the answer of 'a' divided by 'b'?", where we only have answers if the result was a product of a or b with an actual integer. How about negative integers? Show me a negative number. You can't, yet it has utility for when someone finally pays off their debt to know they're square. In fact, show me the number one. You can't, because the difinition of the number one, like beauty, is in the eye of the beholder. A spoon is one as a spoon, but multiple as molecules, even more so as atoms, etc. The only thing you can show me is the number zero because it implies a lack of something to show.

congrats on 314 subscribers