I think my method was an induction, but might have involved contradiction in proving one of the steps.Hi seanieg89. I can get some sort of induction argument going, but was wondering if there is a proof by contradiction. It seems just right for one!?
sorry but can you explain what the question is asking for? I don't know what that last symbol is supposed to mean.
Assuming that the symbol means "for x between and including 0, and 1", I get an integer answer. Is it an integer answer? I'd like post my solution, but only if I'm sure that there's no sillies.
I think this question is beyond the Ext2 course (the whole idea of convex sets and the intersections of such sets).
Do you understand the definition of a convex set in the first sentence?sorry but can you explain what the question is asking for? I don't know what that last symbol is supposed to mean.
This is only necessarily true if:
Let
Okay, so let
Can you post a problem which you found to be quite tough from when you were year 12?Supposewere not true.
Then given such convex sets, we could find distinct points in the plane
such that
is only in the three sets that AREN'T
.
But any four points in the plane define a unique convex quadrilateral Q.
Without loss of generality suppose this quadrilateral has verticesin anti-clockwise order.
Then by convexity, the diagonallies in
and the diagonal
lies in
.
As the diagonals of a convex quadrilateral intersect, that means the point of intersection of these diagonals must lie in every.
This completes the proof of, and hence the whole problem.
I can't really remember off the top of my head. Try some of the problems from olympiads.Can you post a problem which you found to be quite tough from when you were year 12?
Prove that (n+1)^(n+1) + (-n)^n is not divisble by 9 for any natural number n.
How can we have the example ofDefine a function by:
Whereis prime,
is a positive integer, and
is the highest power of
that divides
.
Note thatdoesn't have to be integer. i.e.
You are given that the function defined has t
he property that:
Use this function to prove that the square root of all non-square positive integers is irrational.