Post me your hardest maths question you know

I only do A-Level further maths so anything I ask you can probably do.

Hang on I'll come back with something that I'm doing atm in class
 
Explain the ways in which Russell's paradox can be avoided

Let R be the set of all sets that are not members of themselves. If R qualifies as a member of itself, it would contradict its own definition as a set containing sets that are not members of themselves. On the other hand, if such a set is not a member of itself, it would qualify as a member of itself by the same definition. This contradiction is Russell's paradox. Symbolically:

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without using ZFC :)

Also explain why and how 0=1

Oh and i only did maths for IT in uni last year which was such a bad module :p
 
(1+x^2)dy/dx - (4x^3y/(1-x^2) =1 (-1 < x < 1)

Solve the equation to show that

y = (k + 3x - x^3) / 3(1-x^4)

where k is an arbirtrary constant.

Not hard at all because if I can do it then millions of people can :P

Still looks hard to people who have no clue.
 
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