38
votes
7answers
2k views

When working proof exercises from a textbook with no solutions manual, how do you know when your proof is sound/acceptable?

When working proof exercises from a textbook with no solutions manual, how do you know when your proof is sound/acceptable? Often times I "feel" as if I can write a proof to an exercise but most ...
3
votes
0answers
74 views

My first simple direct proof (very simple theorem on real numbers). Please mark/grade.

What do you think about my first simple direct proof? What mark/grade would you give me? Besides, I am curious about whether you like the style. Theorem Let $I = [a,b]$ be a non-empty closed ...
2
votes
0answers
29 views

On ambiguity in statements expressed in natural language, where the statements use an indefinite article, e.g. “a”.

Please consider the following example statements and judge the meaning of the article "a". Example: A house is a building. Example: A house is being built next to our house. In example 1, "a" is ...
3
votes
2answers
128 views

Real Exponentiation (help with an exercise)

Hi everyone I have serious problems with this exercise. I would appreciate any help. Thanks. (I can use freely any fact regard to real exponentiation when the exponent is a rational number, other ...
36
votes
7answers
3k views

How does a non-mathematician go about publishing a proof in a way that ensures it to be up to the mathematical community's standards?

I'm a computer science student who is a maths hobbyist. I'm convinced that I've proven a major conjecture. The problem lies in that I've never published anything before and am not a mathematician by ...
1
vote
0answers
170 views

Lemma or proposition?

Let statement 1 be an obvious consequence of the statement 2. Let the statement 1 go before the statement 2 in the text. The statement 1 is actually used to prove statement 2. I label the statement 2 ...
23
votes
4answers
911 views

Are there any common practices in mathematics to guard against mistakes?

It occurred to me that math is somewhat like programming (or vice-versa, if you prefer) because, in both, it is easy to make mistakes or overlook them, and the smallest error or misguided assumption ...
0
votes
2answers
103 views

how can I present an idea about the difference between two functions clearly?

I have a presentation in which I want to point out a difference between two functions. Instead of putting the two functions on a slide and pointing to the differences, I want to do something simple. ...