An earnest question about irrational numbers was posted on r/math earlier, but lots of the commenters seem to be making some classical mistakes.

Such as here https://www.reddit.com/r/math/comments/1gen2lx/comment/luazl42/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button

And here https://www.reddit.com/r/math/comments/1gen2lx/comment/luazuyf/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button

This is bad mathematics, because the notion of a "definable number", let alone "number defined by an English sentence", is is misused in these comments. See this goated MathOvefllow answer.

Edit: The issue is in the argument that "Because the reals are uncountable, some of them are not describable". This line of reasoning is flawed. One flaw is that there exist point-wise definable models of ZFC, where a set that is uncountable nevertheless contains only definable elements!

Thread on r/math

Thread on r/mathematics

The user claims to have a proof of the Riemann Hypothesis which has consisted of images of lines and circles and a video of lines moving. My R4 is that this doesn't prove the Riemann Hypothesis, it's hard to be more specific since there isn't really anything resembling mathematics here. They claim their proof is valid because it is a proof by a completely functional projective space and anyone who doesn't understand that is a dumbass.

Added insults to anyone who disagrees with them or points out any problems.

Looks like the posts were just removed, but all their content can be found in the replise anyway. The video is in the r/mathematics link.

This thread was hilarously bad. Apparently those who believe that mathematics was invented, at least in some snall part, have beliefs which "are not typically held by rational people." Enjoy

As per the title. We've recently had a spate of karma-farming bots reposting stuff on this subreddit. Should new rules/mod policies be implemented to deal with these?

The bad math

Explanation of the Monty Hall problem

I found this yesterday while trying to elucidate the reasoning behind yesterdays bad maths, and in retrospect I should've posted this instead because it's much funnier. Our commenter sets forward an interesting argument against the common solution to the Monty Hall problem, the highlights of which are below:

Reality doesn't shift because the number of unopened doors changes. The prize doesn't magically teleport. Your odds of success are, and have always been, random.

The Monty Hall problem is designed as a demonstration of "conditional probability" where more information changes the probabilities.

What it ignores is that one can't reasonably talk about probabilities for individual random events. A single contestant's result is random. It will always be random.

The problem with your logic is that you're assuming that probability theory applies, and that a 2/3rds chance is worse than a 1/3rd chance in this instance. The problem with this is that probability theory doesn't apply here. You can no more reasonably apply probability theory to this problem than you can to a coin toss or even a pair of coin tosses. The result is random.

This is why Monty Hall is an example of the Gambler's Fallacy. You've misunderstood what the word "independent" means in the context of probability theory and statistics. It doesn't have the same meaning as in normal English.

The simple fact is that anyone who knows anything about statistics knows that there's a lower limit below which probability theory simply cannot deliver sensible results. The problem is that people like to talk about a 1 in 3 chance or a 1 in 2 chance, but these are not actually probabilistic statements, they're more about logical fallacies in human thinking and the illusion of control over inherently random situations.

Everyone who watches the show knows that the host will reveal one of the wrong doors after you choose. Therefore there are actually only 2 doors. The one you choose and one other door. The odds aren't 1 in 3 when you start, they're 50/50. Changing the door subsequently doesn't change anything. The result is a coin toss.

My objection is different and has to do with assumptions regarding distribution. The Monty Hall Problem assumes a Beysian statistical approach which in turn relies on a normal distribution.... which is nonsense when someone is only making two choices. It just doesn't work and violates the assumptions on which the Monty Hall Problem is based.

And the Monty Hall Problem makes this mistake too. I can grasp the fundamental point the Monty Hall Problem is trying to make about conditional probability, but given that I have to spend weeks training students out of this "singular events are probabilistic" thinking every bloody year I can't forgive the error.

R4 - Where do you even start? Probability does apply to single events, and 2/3 chance is in fact higher than 1/3 chance. Monty opening a door provides additional information to the player, meaning the second opportunity to pick a door is not independent so Gamblers fallacy is not relevant. The host opening a door does not mean that there are "actually only two doors". The Monty Hall problem can be solved by writing out the possible outcomes on a piece of paper - the problem does not require a Bayesian (or "Beysian") approach, and the Bayesian approach itself does not rely on a normal distribution.

The bad maths

The article

The posted article reports a significant correlation between the frequency of sex between married couples and a range of other factors including the husbands share of housework, religion and age.

One user takes bitter issue with the statistical findings of the article, as well as his other commenters. Highlights:

I suspect the writers of this report are statistically illiterate

What also makes me suspicious of this research is when you scroll down to Table 3 there are a mass of *** (p<0.01 two-tailed) and ** (p<0.01). As a rule of thumb in any study in the social sciences the threshold for a statistically significant result is set at p<0.05 because, to be frank, 1 in 20 humans are atypical. It's those two tails on either side of the normal distribution.

To get one or maybe two p<0.01 results is unlikely but within the realms of possibility, but when I look at Table 3 I count 51 such results. This goes from "unlikely" into the realm of huge red flags for either data falsification, error in statistical analysis, or some similar error. 

And 51 results showing p<0.01? That's "winning the lottery" territory. No, it really is. This is again just simple statistics. The odds of their results being correct are well within the "trillions to 1" realm of possibilities.

If your sample size is 100, 1,000, or 100,000, there should be about 1 in 20 subjects who are "abnormal" and reporting results that are outside of the normal pattern of behaviour. The p value is just a measure of, if you draw a line or curve, what percentage of the results fall close enough to the line to be considered following that pattern.

What the researchers are fundamentally saying with these values is that they've found "rules" that more than 99% of people follow for over 50 things. If you believe that I have a bridge to sell you. 

If only 1 data point in 100 falls outside predicted pattern (or the "close enough") zone then the p value is 0.01. If 5 data points out of 100 fall outside the predicted pattern then then p value is 0.05, and so on and so forth.

R4 - Misunderstanding of significance testing

A P value represents the probability of seeing the observed results, or results more extreme, if the null hypothesis is true. The commenter misconstrues this as the proportion of outliers in the data, and that the commonly used p<0.05 cutoff (which is arbitrary) is intended to represent the number of atypical people in the population.

The claim that reporting 51 significant p values is equivalent to winning the lottery is likely based on the further assumption that these tests are independent (I'm guessing, the thought process isn't easy to follow).

https://www.youtube.com/watch?v=gSdNwDVdKTo

R4: classic "I've solved math" energy here. The person discuss why infinity MUST BE the multiplicative inverse of zero, and that otherwise any number would be infinite. And his theory is """sound""" because of focal points of lenses apparently. Pretty sure that all the physical stuff is pretty bad as well...

Here's a theory I had for a while that I posted as a comment before to a different subreddit so I'm gonna repost it here with some changes and expansions for karma: math is a donut because 1/0=±∞ (1/.1=10 so the smaller it is the larger it becomes however this also applies to 1/-.1=-10) and since there are no square roots or variables here it is not a case of values being multiple things so that means that the entire concept of math loops at ∞ so ∞+1=-(∞-1) so also ∞=-∞ which is also true for 0 so math is a ring shape otherwise know as a donut shape or if you want to get technical then a torus. This also makes a bit of a problem with this theory because it means ∞+∞=0 so 0/2=∞ although this could mean ∞=0 and negatives are just really big the problem is that 3∞=∞ so 0/3≠∞ this problem is created because both 0 and ∞ technically aren't real since it is impossible to have infinite of something or absolutely nothing, and I got no idea how to stretch this idea farther however you can connect liner or whatever the 1/x graph is called to themselves showing what they would look like with this (I think quadratic might also work however it is harder to create with this).

https://preview.redd.it/k5d415lio10d1.jpg?width=940&format=pjpg&auto=webp&s=af479b630f85c451494dff8f7b2eee356184728f

R4: It is not "infinitely difficult" to prove that a number is infinitely long; there exist many relatively simple proofs of the existence of numbers of infinite length. It is also not known whether pi contains every possible finite string of digits in base-10.