8 minutes of Counterintuitive Math

The birthday paradox is one of my favorite paradoxes because it feels so wrong, yet it's mathematically sound.

Every fiber of my being disagrees with p-adic numbers

99999... = -1 because the simulation running our universe is on a twos-complement machine.

...9999 isn't equal to -1 because the two are different types of numbers Using p-adic numbers with real numbers allows you to falsely “prove” any ...nnnn = -1 conclusion, where “n” stands for a single digit. For example in the 2-adic system where numbers are written with the digits 0 and 1 (e.g. 10 = 2, 11 = 3, 100 = 4) you could show: ...1111 + 1 = 0 => ...1111 = -1 This too would be false because p-adic numbers don’t follow real number arithmetic. Rather, the problem should be written as: ...9999 + ...0001 = ...0000 ...0000 != 0

It's crazy how barely anyone has seen this

I mean a 99% water-content potato is just a glass of water with some starch sprinkled on it. So a 50% change to dry-weight really isn't too much

These don't feel like "proofs", it just feels like our standard mathematical system has core deficiencies.

not only did you give a short introduction of proof of 0.9…=1 in just shy of 30 second, but you also explained in the RIGOROUS manner, I am impressed already.

Missing an explanation for some of these

Absolutely beautiful how you just get to the point without wasting everyones time. If more youtubers were like that the plattform would be so much better

I was thinking 0xffffffff is -1 because it's a signed integer.😂

In a room of 367 people, there is a 100% chance that someone has the same birthday

only 300 views? before i saw the views i really thought it has hundreds of views because the animations are just like those other good math videos with a lot of views... how can this channel also only has less than 2k subs??? it deserves more than hundreds of thousands...

The last one is tricky since the median i.e. the most common result is very different from the average if I remember correctly.

This video deserves way more attention, it's great

The periodic numbers one isn't actually true, as it is actually just a semantic argument that relies entirely on the ways we write numbers rather than the actual value itself. Sure, if you add it by continuosly getting a zero and carrying the one, you will get an infinite amount of zeros, but you'll also never finish this calculation. It'd be like if you added 1 to a hundred digits of 9s, but stopped halfway and claimed it equaled 0. If you just finished the calculation, you'd eventually get a 1 in the first digit. Same with the infinite one, just that you can never finish the calculation. Not only that, but this trick only works because we use a base 10 system, which is an arbitrary choice. If you converted the infinite 9s number to hexadecimal and added 1 to it, you would no longer get an infinite amount of 0s and would instead get something entirely different which obviously does not equal -1. Instead, this trick would work with an infinite amount of Fs in hexadecimal.

2:55 i also got 2/3 but i think the core of the problem is understanding the question. the question asks for the probability of the second ball is red WHEN the first ball is red. so the first ball can not be green this is different than a question saying: out of these 2 boxes, what is the possibility of getting two reds? then the probability wouldn't be independent of each other and would be 1/2 at least i think idk

I loved this video, the graphics and the subtitles really elevate the script. Youve gained a subscriber!!

The probability problem is all based on the wording, both 50% and 66% are correct depending on the wording. "Let's take the ball out of the random box, the ball is red. What is the probability that the 2nd ball in this box is also red?" This kind of setup leaves the question open to ambiguity around whether or not the ball was chosen randomly, or if just the box was. "the random box" implies the box is what was random, and 'take the ball' implies it was specific. Assuming it's all random, there a 50% chance to pick A or B. A red ball from A is 50%*50%=25%. A red from box B is 50%*100%=50%. A 75% chance total to pick a red, 25% from A, 50% from b, or 2/3, 66% that you picked box B, which will result in double reds. However, if you assume just the box was random and we chose to take the red ball first. The ball left in the box would either be Red or Not. If this ball was picked from A, there is a 0% chance the remaining ball is red. If it was picked from B, there is a 100% chance the remaining ball is red. This results in a 50% chance that the ball was from A or B. This shows the importance of being extremely clear with and direct with probability. Most of the confusion in probability comes from wording, not the maths itself.

The idea that an infinite string of 9s, written as "...999999999" (with an infinite number of 9s going off to the left), is equal to -1 is a speculative and controversial concept in number theory.