# Questions tagged [formal-proofs]

For questions about proofs within a formal system, such as natural deduction or Hilbert system.

537 questions
Filter by
Sorted by
Tagged with
2answers
199 views

### Can't understand this set theory proof.

I read the proof of a 'set theory' equation from a website called Meritnation. But I can't understand the proof after 30 minutes of trying and even find some mistakes in it. This is the proof(I have ...
2answers
90 views

### Determining the correctness of a formal proof

Is the following formal proof, proving $\forall A\forall B \forall C[A+C=B+C\Longrightarrow A=B]$ correct?? Proof 1) $a+c=b+c$.............................................................Hypothesis ...
1answer
2k views

### Proving that two expressions are equivalent

So, I'm working through some proof exercises, and one of the questions is about the following regular expression: (a|b)* = a*(a|b)* if they are equivalent, prove ...
1answer
85 views

### Another topology question

This is a two part question. The first part, part (i), I present with the solution I reached. The second part, part (ii) is where I need help. (i) Let $B$ be a basis for a topology $T$ on a non-empty ...
2answers
2k views

### equivalence between formal and informal proof

I'm reading Cohen's book on the independence of the continuum hypothesis, and I see that all the proofs that he gives when he's defining the basic notions of set theory (ordinals, cardinals, ...
1answer
87 views

### Prove formally that $\frac {n^2 + 2}{3n^3 - 5n}\to 0$ as $n \to \infty$.

I'm reviewing some Sequences notes from a Mathematics Analysis course I'm taking. I'm finding the beginning of the formal proof below confusing. Some clarity on the following questions would be much ...
3answers
287 views

1answer
171 views

### Should $x$ be not free in $\beta$ to prove $\vdash [ \forall x(\beta\rightarrow \alpha)\rightarrow (\exists x\beta\rightarrow \alpha)]$?

Should $x$ be not free in $\beta$ to prove $\vdash [ \forall x(\beta\rightarrow \alpha)\rightarrow (\exists x\beta\rightarrow \alpha)]$? In "Mathematical Introduction to Logic, Enderton" This is an ...
1answer
107 views

1answer
434 views

### Linearly Independent Set Proof

If S = {${v_1,...,v_n}$} is a set of vectors in $R^n$ such that no $v_i$ is a scalar multiple of $v_j$ with $i≠j$, then {${v_1,...,v_n}$} is linearly independent. So far, I've used the ...
1answer
592 views

1answer
357 views

### Status of declarative proof languages in proof assistants

I'm interested in formalising mathematics and logics in a proof assistant, both to get to know a proof assistant and to make an archive of proofs for myself (nothing too fancy, mainly first order ...
1answer
173 views

0answers
594 views

### A simple proof of Descartes's rule of sign

I search all over the Internet for a proof of Descartes's rule of sign. Found a pdf file which has page-long proof that a high schooler has to no way to understand. Can somebody talented here give ...
2answers
2k views

### Proof of a theorem in Hilbert's system

I have been trying to prove that the propositional formula $\big( \alpha \rightarrow \lnot \beta \big) \rightarrow \big((\alpha \rightarrow \beta) \rightarrow \lnot \alpha \big)$ is a theorem in ...