/sci/ - Science & Math

Why are numbers?

Why is mathematics plural? What is a mathematic?

>>3964557
Prove that the set of real numbers cannot be put into bijective correspondence with the integers.

>>3964557
2 + 2 = 22?

Pick's Theorem states that the area of a simple lattice polygon P is B(P)/2 +I(P) - 1, where B(P) is the number of lattice points on the boundary of P and I(P) the number of lattice points in the interior of P.

Prove Pick's Theorem for an arbitrary lattice rectangle with sides parallel to the x and y axes.

>>3964570
Prove that for every integer n > 1 there is a prime p such that n<p<n!+2

Prove that the null space of a bounded linear operator is closed.

>>3964572
Would it be along the lines of:
Z is contained in R.
Map all Z to all Z's in R.
pi
?

Solve the heat equation Ut = kUxx in the region 0<x<L, t>0 where;
U(0.t) = 0
U(L,t) = 0
U(x,0)=100sin(3pix/L)

>>3964590
No. You should note that Z CAN be put into bijective correspondence with Q, despite Q containing Z

>>3964590
Here's a hint. Think about infinite decimals and suppose a bijection did exist.

integers are countabe, reals are not?

>>3964650
That's what the question is asking you to prove.

op here
thanks, I love putting off required maths to do unrequired maths.

>>3964669
To put it in a way that isn't a terrible meme - I know exactly what you mean.

what is divided by zero?

>>3964800

>>3964587
something along the lines of..
it's linear, its continous, its continous at 0, its invertible, the complement of that domain is open?

>>3964821
Well the last point you made
>the complement of that domain is open?
Is proof that it is closed, so if you can show that to be so you're done.

However if I were you I'd be thinking about limit points.