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73 votes
16 answers
15k views

Why can a real number be defined as a Dedekind cut, that is, as a set of rational numbers?

8 votes
3 answers
883 views

Why is my alternate method of calculating scalar products not working?

7 votes
4 answers
1k views

What is the simplest way to rigorously define division (why does the standard algorithm work)?

6 votes
2 answers
405 views

$ \int\frac{g(x)}{f(x)} \, dx $ where $f(x) = \frac{1}{2}(e^x+e^{-x})$ and $g(x) = \frac{1}{2}(e^x - e^{-x})$?

5 votes
2 answers
1k views

Why don't I get the correct limit of a sequence, regardless of how I arrange it (the sequence), while following the rules for solving limits?

4 votes
2 answers
225 views

What are some fun nonstandard models to explore?

3 votes
1 answer
150 views

Is $\forall x \square \varphi \leftrightarrow \square \forall x \varphi$ a valid formula for all formulas $\varphi$?

3 votes
3 answers
639 views

Formal definition of definite condition of membership $\in$ in set theory?

3 votes
1 answer
762 views

What are "parameters" in a formula of first-order logic?

3 votes
2 answers
125 views

Is this a proper translation of $\exists x(\emptyset \in x)$ into $\mathcal{L}_{\in}$?

3 votes
5 answers
167 views

Find such a complex number $z$ so that $|z| - 2 = z +12i$

2 votes
2 answers
61 views

What is the maximum total displacement needed for sorting a list? [duplicate]

2 votes
2 answers
113 views

Do all mathematical and logical axiomatic systems implicitly ground natural numbers?

2 votes
1 answer
100 views

Please double-check my deduced equation

2 votes
2 answers
327 views

Help me understand criteria for $\triangle ABC \sim \triangle A'B'C'$

2 votes
2 answers
54 views

Why is binary compositum $T \circ R$ defined as $\{ (x,y); \; (\exists u)(xRu \wedge uTy) \}$?

2 votes
2 answers
133 views

Conceptual issue with indefinite integrals and the meaning of $dx$

2 votes
1 answer
93 views

Defining the indexed union/intersection formally in $\mathsf{ZFC}$

2 votes
0 answers
137 views

Confusions regarding the metatheory

2 votes
0 answers
69 views

A problem with the definition of limit for functions of the form $f : \{ a \} \to \mathbb{R}$

2 votes
1 answer
90 views

The probability of throwing the same value (value not fixed) on a $N$-sided fair die at least $k$ times in a row at $n$ throws

2 votes
2 answers
122 views

Are these proofs of two Halting Problems rigorous?

2 votes
1 answer
80 views

Can this anomaly of the unary base system be generalized?

2 votes
0 answers
86 views

Did I successfully map every proof tree to a formula?

1 vote
0 answers
57 views

Is this proof about associativity correct, and can we simplify it?

1 vote
1 answer
42 views

Issue with calculating a probability with the standard normal table

1 vote
1 answer
54 views

Formalizing the intuitive existential elimination

1 vote
1 answer
52 views

Is the claim that $\mathsf{Rel}$ (the class of set-theoretic relations) is a category false?

1 vote
0 answers
74 views

Verifying that some maps are functors

1 vote
1 answer
44 views

The definition of the semantic consequence relation for modal logic