We have a equivalence relation on [0,1] × [0,1] by letting (x_0, y_0) ~ (x_1, y_1) if and only if x_0 = x_1 > 0... then how do we show that X\ ~is not a Hausdorff space ?
In a first countable space any point that is adherent to a set S is also the limit of a sequence in S.
In my head, this seems obvious, but I can't seem to get it on paper.. I know that is has to do with inverse functions preserving unions and intersections, but can't seem to write the proof out.
I came across this Proposition in my book, and I know it's something really simple that I'm missing, but I can't seem to prove it.
Let n be an odd composite integer.
a) n is a pseudoprime to the base b where gcd (b,n)=1 if and only if the order of b in (Z/nZ)* divides (n-1).
b) If n is a...
I've been trying to work out a bunch of problems that have to do with finding irreducible polynomials, and this one really seemed to stump me...
What is the probability that a random monic polynomial over F_3 of degree exactly 10 factors into a product of polynomials of degree less than or...
So I came across this problem in my textbook, but couldn't seem to solve it...
Let n be any squarefree integer (product of distinct primes). Let d
and e be positive integers such that de — 1 is divisible by p — 1 for every prime divisor p of n. (For example, this is the case if de...