/sci/ - Science & Math

Say that I have some set [math]X[/math] and some set [math]Y[/math]. If I know that two functions [math]f, g[/math] satisfy

[math]f(x) \leq g(y) \; \forall \; x \in X, y \in Y[/math]

then does it follow that

[math]\mathrm{sup}_{x \in X} f(x) \leq \mathrm{inf}_{y \in Y} g(y)[/math] ?

If so, why?

I am finally excepting that i fucked up
I listened to my parents and instead of entering in STEM field i end up in business administration,yes its one of the best economic universities of my country,but i don't like it lads.
I am 23 and i still trying to get the fucking degree mostly because i am not interested about the courses except if has something to do with statistics.
I am planing to get the fucking degree and then straight away get into mathematics.
I know i am kinda late but hell, i feel so fucking incomplete without maths.
This is wrong guys, can you please give me any suggestions or your thoughts about this?
Ps yes i am a retard, i know

>>10210745
>The teacher uses molar fluxes (MJ) and mass fluxes (mJ) as
[math]_{M}J_{i}=C_{i}(U_{i}-U^{M})\\
_{m}j_{i}=\rho_{i}(U_{i}-U^{m})\\[/math]
>and he told us to proof these (just transform the right side into the left), asumming only A and B components
[math]_{M}j_{A}+_{M}j_{B}=\rho(U^{m}-U^{M})\\
_{m}J_{A}+_{m}J_{B}=C(U^{M}-U^{m})\\
_{M}J_{A}=-(\frac{\rho^{2}}{cM_{A}M_{B}})D_{AB}\nabla\omega_{A}\\
C(U_{A}-U_{B})=-\frac{cD_{AB}}{x_{A}x_{B}}\nabla x_{A}\\[/math]
I have some problems

>taking exam
>30% is like twenty T/F questions and the other 70% is proofs
>T/F Section Guidelines: correct answer: +4pts, incorrect answer: +0pts, leave space blank: +2pts.
>see graded exam
>aced the proofs section with flying colors
>mfw I missed every fucking T/F question

>graduate with a phd in math
>haven't even studied 90% of the shit that US students learn to pass their fucking quals and be considered for a phd
why is maths education so shit in the UK. at least I'm done with a phd at age 25 though, but it still sucks because I know fuck all.

Alright /sci/, brainlet here. Redpill me on the Boltzmann Brain. Wtf is that shit, explain it in layman's terms

Pic unrelated