Tagged Questions

1
vote
2answers
163 views

Ratio when one entity is 0.

What is the ratio between boys and girls in a group with 30 boys and 0 girls? Is it 1:0, 30:0 or something involving infinity and undefined? Can somebody help me out here?
3
votes
3answers
134 views

Continuity of $f(x)$ involving infinity

$f(x)= \frac{\sin(\pi x)}{x(1-x)}$ How can I define $f(0)$ and $f(1)$ to make $f(x)$ continuous on $[0,1]$? I've found that the limit at $0 = \pi$, and the limit from the left at $1 = \infty$. I ...
1
vote
5answers
375 views

Prove the set of functions $f : \mathbb{Q} \rightarrow \{1,2,3\}$ uncountably infinite

Prove that the set of functions $f: \mathbb{Q} \rightarrow \{1,2,3\}$ is uncountably infinite. I'm totally stuck on this one. We have just been shown Georg Cantor's diagonalization argument in class ...