# Tagged Questions

For questions about the formulation of a proof, not about the mathematics behind it.

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38 views

1answer
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### Proofs problem with bijection [closed]

Let $f : A \rightarrow B$. Prove that if $X \subseteq A, Y \subseteq B$, and $f$ is a bijection, then $f(X) = Y$ if and only if $f^{-1}(Y) = X$.
4answers
45 views

### A surjective map $S \to T$ implies $|S| \geq |T|$

Problem: Suppose that there is a function mapping $S$ onto $T$. Show that $\operatorname{Card}(S)\ge\operatorname{Card}(T)$ Issue: I can't seem to find a reason why this follows. If $S$ maps $T$...
1answer
122 views

### Show that the set of polynomials with rational coefficients is countable.

Problem: Show that the set of polynomials with rational coefficients is countable. Idea: We know that the set of rational numbers is denumerable. This implies that the set of rational numbers is ...
1answer
33 views

### Square of an odd integer is odd, square of even integer is even, what is the case for higher powers?

Are there rules for higher powers? It seems like even and odd is preserved by powers, but how do I prove that?
6answers
67 views

### Induction Proof with Fibonacci

How do I prove this? For the Fibonacci numbers defined by $f_1=1$, $f_2=1$, and $f_n = f_{n-1} + f_{n-2}$ for $n ≥ 3$, prove that $f^2_{n+1} - f_{n+1}f_n - f^2_n = (-1)^n$ for all $n≥ 1$.
2answers
46 views

### Prove that if the complex function $|f(z)|^2$ is constant in $D$ and $f(z)$ is analytic in $D$, then $f(z)$ is constant in $D$.

My proof: Let $|f(z)|^2 = M$ for $z\in D$. Then $f(z) = \pm\sqrt{M}$ (not sure about this step, are there only two values for the square root of a complex number> No right? Could be more. But I don'...
1answer
32 views

### Let $f: A \rightarrow B$ and $g: B \rightarrow C$ be functions. If $f$ onto and $g$ is not onto, then $g \cdot f:A \rightarrow C$ is not onto

I need help with this proof. I claim it is true, and I want to prove it directly using the definition of onto. Proof: Let $A,B,$ and $C$ be sets, and let f, g be functions s.t. $f:A \rightarrow B$ ...
3answers
74 views

### Proof using formal definition: Infinite limit

I was wondering how get the proof of this limit: $$\lim\limits_{x\to -\infty}\dfrac{{x^2} - x + 1}{x + 4} = -\infty$$ The problem is that I don't know what to do for find the appropriated values to ...
4answers
922 views

### Proof: Is there a line in the xy plane that goes through only rational coordinates?

Question: Is there a line in the XY plane that has all rational coordinates. Prove your answer. Idea: There is most certainly not. I believe it can be shown that between any 2 rational points that ...
1answer
180 views