Recent content by d_leet

I'm pretty sure that it is, in fact, always true.

Note that 9 is congruent to 4 mod 5.

Simply connected is by far a more specific condition than either of which you mention. Simply connected means path connected, and a trivial fundamental group. No representation as the disjoint union of two open subsets is referred as Connectedness, and if there exists a path between any two...

Ok so pick k=1 for all epsilon.

It's

You have an infinite union of open sets which cover some compact set X, you wish to show that finitely many of them suffice to cover X.

I'm fairly certain it means closed in the topological sense as a subset of the Lie group G.

Once you map a generator somewhere you fix where every other element in the group goes. You can't map say a to b and a^3 to b^5 with one homomorphism because the first implies that a^3 must map to b^3.

This is certainly not the way to approach the problem. The biggest hint is basically given to you in the problem that the scores are distributed normally.

As you have defined g, unless you know more about f, then g is only defined at 0 and no other points in [0,2]. I mean g(1)=f(1+2)-f(1)=f(3)-f(1), but what is f(3)? And how does what you have written show that f(1)=f(2) certainly there are continuous functions on [0,2] with f(0)=f(2) but that...

Learning topology requires some knowledge of basic set theory, but little more than that.

f(x)=x is surjective (and injective), g(x)=-x is also surjective (and injective), what is the sum of f and g?

You are certainly correct that there are other algorithms that would generate this same sequence for the first few terms. So strictly speaking the next number could be anything. Ironically though if you continue you the sequence with your pattern you will arrive at exactly the same sequence the...

Is this true? Almost every group theory book I have looked at proves the uniqueness of the identity as a theorem.

What do you consider a number theorem to be?