# fact

1. ### Proving an intuitively obvious fact

I have a lot of trouble proving very simple, intuitively obvious facts. I want to prove the following: Every set that contains an infinite subset is infinite. I don't even know where to begin to argue this. Could someone show me the right way to approach this? Thanks.
2. ### Given that 907 and 997 are primes, use the fact that 907 equiv -997 (mod 28) to calcu

Given that 907 and 997 are primes, use the fact that 907 \equiv -997 \pmod{28} to calculate \left( \frac{7}{997} \right) - \left( \frac{7}{907} \right) . I am a bit confused about the question to start with, is \left( \frac{7}{997} \right) - \left( \frac{7}{907} \right) about fractions or...
3. ### Using the fact that a pair of numbers is relatively prime to prove that one is prime

The GCD(30030, 257) = 1 Using that fact, and the prime factorization of 30030 = 2 * 3 * 5 * 7 * 11 * 13 How can I show that 257 is prime. I'm not sure this is true, but is it because all non-prime numbers have a prime factorization, and since 30030 and 257 are relatively prime (only have a...
4. ### Inferring a fact from a simple line graph (Multiple Choice Question)

Dear all, I am having some trouble answering this multiple choice question on a graph and have posted the question with my thoughts below. Thank you very much. scherz0 --- Given correct answer (hidden in white): D My thoughts: According to the question, y-axis =...
5. ### Problem understanding a fact

Hello ! I have troubles understanding this statement : I don't understand why there is 0.5 probability to find a nontrivial factor of n, since if we call p one factor of n, then if we find a nontrivial factor, p must divide a \pm b, and so there are \frac{n}{p} possibilities that this...
6. ### Fibonacci numbers - An interesting fact

I picked up this problem in one of the posts in this forum only. Let F1 = 1 F2 = 1 F3 = 2 F4 = 3 .. Fk = .. .. so on Be the Fibonacci Series. Prove that for any natural number number n, there exits infinite Fibonacci numbers that are multiples of n. I have spent quite some time on this...
7. ### prove some cardinalities fact

Prove that (a,b)^u = a^u * b^u for all cardinalities a,b, and u also prove that if a <= b , then a^u <= to b^u how do you prove these facts? I have no idea how to start the prove
8. ### prove some cardinalities fact

Prove that (a,b)^u = a^u * b^u for all cardinalities a,b, and u also prove that if a <= b , then a^u <= to b^u
9. ### Surface area problem (in fact, more of a parametrization problem...)

Hi all, The cylinder x^2 + y^2 = x divides the unit sphere S into two regions S1 and S2, where S1 is inside the cylinder and S2 outside. Find the ratio of the Areas A(S2)/A(S1). I know the surface area formula, but I can't seem to find a parametrization of the said surfaces that works! The...
10. ### Fact check

Just to make sure, I am pretty sure that I am right but \text{ As }x\to{0}\csc(u(x))\sim\frac{1}{u(x)} Provided u(0)=0 Here is how I decided upon that \lim_{x\to{0}}\frac{\csc(u(x))}{\frac{1}{u(x)}}=\lim_{u(x)\to{0}}\frac{u(x)}{\sin(u(x)} Now let \psi=u(x) and as...