# Tagged Questions

Questions asking for a "big list" of examples, illustrations, etc. Ask only when the topic is compelling, and please do not use this as the only tag for a question.

199 views

### What does Hartshorne do wrong?

I'm currently trying to learn algebraic geometry from Hartshorne's Algebraic Geometry. I've often heard it said, both on MathOverflow and in my department, that Hartshorne's treatment of certain ...
15 views

### Examples of generalized geometric series.

I'm preparing a short presentation on the convergence of the geometric series of matrices, and I'd love some examples of their uses. I've encountered them when approximating inverses of matrices ...
70 views

### Theorems relating to the limitation of mathematics

At one point, mathematicians believed that they may be capable of expressing all of mathematics in one system of ideas, and that their abilities were unlimited. Unfortunately, things like the Godel's ...
149 views

### Examples of bi-implications ($\Leftrightarrow$) where the $\Rightarrow$ direction is used in the proof of the $\Leftarrow$ direction.

[I'm asking for examples of proofs with a certain structure. There is quite a lot of text before arriving at the questions. This is because asking for examples of a phenomenon is best carried out by ...
248 views

### Is there a property in $\mathbb{N}$ that we know some number must satisfy but don't know which one?

I have two questions. $(1.)$ Is there a property of the natural numbers such that we know at least one number satisfies it but we don't know which one? Even more, $(2.)$ Is there a property ...
2k views

### Unconventional mathematics books

I've recently purchased Oliver Byrne's reproduction of Euclid's Elements. It's a beautiful tome, that's rather unique in its presentation of the material as it represents many of Euclid's proof as ...
92 views

### Exercises on group theory [closed]

What are some difficult, challenging and fair exercises in group theory? I know it is quite general, in particular I am referring to these areas of group theory: theory of automorphism group ...
608 views

### $2=1$ Paradoxes repository

I really like to use paradoxes in my math classes, in order to awaken the interest of my students. Concretely, these last weeks I am proposing paradoxes that achieve the conclusion that 2=1. After one ...
215 views

### How many six digit numbers start with the same two digits and end with the same three digits?

Say that there is a 6 digit number the first digit is not allowed to be 0 or 1 so How many number combinations start with the same two digits and end with the same three digits ie.119333, 448222, ...