u/VasyokGregoriy2017

like really, don't tell me i am the only one who catches it happening everyday

Here I am not talking about just starting from ZFC. I am talking about starting from logic foundations and Godel. Do you think that a mathematician that is not someone completely focused on logic can have a complete understanding of all the foundations needed to prove the theorems they currently tackle.

You can think of it like this: Imagine you gave Terence Tao (or any other mathematician that is not purely focused on logic) a theorem that he proved, then you give him an infinite amount of time to prove it from the very basic assumptions about first-order logic and axiomatic systems with one rule: you can't learn anything new, use the knowledge that you already have.

Will he be able to do it?

I don't want to ask about how to prove it here, mathstack exchange exists for it, instead I wanted to share my experience and ask if anyone relates and what you usually do at times like this...

I have been progressing in my book on real analysis really fast but then there was just one theorem and I just hit a ceiling, I just can't prove it.
I am trying to do it for a week now, and I feel like I am doing something useless. It feels so frustrating when you had rapid progress and then just one hard theorem breaks the flow.

It's not like I am bored by it, I am just sad because I had other goals, but this thing just ruins them.

Hi, I have a two-block haircut. When I dry it I might consider either drying my hair upside down, which is the easiest way, or I can dry it by elevating the roots with my hands.

Drying my hair upside down creates texture in places where I don't want it, while elevating the roots is not as reliable because some hair gets dried without being elevated, which is pretty bad.

What do you personally prefer when using a hair-dryer?

My failed attempt of making a 2-variable sequence with it being graphed only on x=y while we need it to be graphed on the while x-y plane

I have been trying to make plots of 2-variable sequences in desmos. I was trying to use 2 arrays of numbers K=[0,1,2,...n] and plotting it like this (K_{x},K_{y},a(K_{x},K_{y})), (K_x, K_y) does not give all the x-y plane, only that x=y line, which was pretty much expected.

Any help would be appreciated.

Here's the link to the graph in the picture https://www.desmos.com/3d/d00gr01lty

From my experience serious bullying is taken seriously, for example physical bullying will actually get the bully in a lot of trouble, however, only a tiny fraction of actual bullying is like this.
Most of the bullying is more like just being annoying or unwelcoming to some other person, calling them names, throwing erasers at them etc, and I was outraged seeing by how even the best teachers simply ignored it.
I had a boy in my classroom that was getting bullied like this. Once he said something during a class. It wasn't anything bad, he was just talking to his friend. The teacher asked him to be quite and the bully just said out loud "shut up" purely to show dominance or idk. The teacher just moved on with the lesson. The problem is that this was happening everyday and everyday it was going this way, what is wrong with these teachers?? They talk constantly about how it's really bad that there is bullying in finnish schools, while some do not intervene at all. If the victim is not being beaten up it doesn not mean that bullying does not need intervention. For example no intervention here resulted into the victim getting into a fight with the bully after constant naming.

Of course rigor is important, but visual intuition is important too, but some real analysis books just don't use pictures at all, for example Terence Tao's book Real Analysis I.
For example the definition of the Riemann integral with upper and lower sums, it is so fruity when you draw it, but for some reason at least in my book it's not being done, I will tell you that there are no pictures at all, not a single one!
But honestly it seems like it kind of sparks you to draw the pictures yourself and if you are actively learning you sure will do it and you must do it, still sometimes it would be convenient to have some visual intuition being done for you. I expected it because Terence Tao said that visual intuition in math is important, but it feels like he left it to the lecturers doing courses based on the book.