2 * ( 2 + 3 = 10

We would be tempted to think that a closing bracket is missing and, correcting the mistake, the proposition would be true. But maybe there is an extra opening bracket, and so this would be a valid but false proposition. That's why, in my opinion, we shouldn't talk about the meaning of an invalid statement. Anyway, I read Bolzano's theorem proof in your site and I really enjoyed it. I took calculus last semester and when my teacher though the theorem (with no proof) I thought "how someone actually proved this?". Now I know There are some other proofs that I would like to see but I couldn't get (even searching the net), so maybe you could tell me where I could find them. I am looking for:

Limit formal definitions (including infinite limits)
Limit laws proof (such as lim a + lim b = lim (a+b) )
Weirstrass theorems

If you know a website with that, I would be grateful for the information.

Bye.
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José Luis Romero

You make a valid argument. I just would approach that sentence from a lighter side of mathematics. You did not have problems detecting and fixing two mistakes, did you? The resulting sentence conveys the intended meaning of the original one. Formally speaking you are right, but whether you should be formal or not is a matter of attitude.

My attitude is that people make mistakes all the time, in speech as well as in writing. This does not mean that what they say has no meaning.

You ask about some formal mathematics sit's. You can find much about limits at https://www.shu.edu/projects/reals/index.html.

I do not know of a place that covers Weirstrass' theorem.
I tried searching at https://www.maths.usyd.edu.au:8000/MathSearch.html|MathSearch>. For "Weirstrass theorem" there are too few references. For "Weirstrass' theorem" there are too many. Try to refine the search. There might be something.

All the best,
Alexander Bogomolny