/mg/ math general: LMFDB edition

What are you studying today, /mg/?

lmfdb.org/universe
>The top half of the diagram is based on the Langlands program, which predicts that any motivic object corresponds to an automorphic object via their L-functions.

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lmfdb.org/EllipticCurve/Q/150/c/1
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I don't really understand how to correctly translate a natural language sentence into propositional logic

>The definition for a bijective function is that the function is both injective as surjective

should it be
[math]I \wedge S \implies B[/math]
Or
[math]I \wedge S \equiv B[/math]

the second

but why?

If it is injective and surjective, it is a bijective function.

How do integrals work? Why can we take the antiderivative of a function f and then have that F(b) minus F(a) is the area of f between those points? I know it’s true but why? Is there an explanation for dumb me who has only done calculus? I know you’re adding infinitesimal rectangles but how does this relate to the antiderivative?

How do I solve for d, where p is a large prime?

[-1 = 5^d] mod p

Thanks from terrible-at-crypto user

how do I prove that (3/2)^n > n by mathematical induction, help

That is just what the fundamental theorem of calculus says. If you want to know why then read the proof.

prove the base case then prove the induction step