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1. Random Thoughts part 6

Guns n'Roses changing it's name to attract the Math, Logician crowd: Guns if and only if Roses.
2. Random Thoughts part 6

In France, Marseille 1, nothing Tolouse.
3. Random Thoughts part 6

I'm still unable to drink fluids to take care of a cold. Liquids, yes. Gases, not quite yet.
4. Collection of Lame Jokes

Same with me pointing out in Bruno Mars' video " It will Rain", that morphine is used for physical, not emotional, pain. No wonder I'm writing this comment from my home on Friday night , while all others are out in bats, clubs.
5. Collection of Lame Jokes

Now no one will be able to steal the wall:

7. Collection of Lame Jokes

Recent causes
8. Collection of Lame Jokes

High-level discussion on the web, as usual

10. Complex numbers confusion (how they got this expression in orange to become -1)

Well, part of the issue is that exp(z) plays a role when dealing with Complexes, e.g., Polar representation, but it's not 1-1, and as such has no global inverse log. This requires you to patch together local inverses. A mess. Edit: Here the square root too, may involve arguments, branches, and...

13. V Space With Norm $||*||$ - Fourier Series

 _always_ works. you just need enough of it ;).
14. B Dividing by infinity, exactly, finally!

Sure, https://en.wikipedia.org/wiki/Compactness_theorem Through the concept of Elementary Equivalence , aka, the Transfer Principle, 1st -order properties are preserved "upwardly", from lower to higher cardinality, between models of different cardinality. Edit: Is that what you were asking?
15. B Dividing by infinity, exactly, finally!

You only need to check through ## \aleph_0## models of the Reals , per Lowenheim -Skolem. Outside of the standard Reals, you lose " standard " metrizability, since metric are Real-valued.
16. B Dividing by infinity, exactly, finally!

Figure it out and you'll get a Figure one out and go collect your Fields/Abel medal.

19. Collection of Lame Jokes

You aint nothing but a Groundhog.

21. Complex numbers confusion (how they got this expression in orange to become -1)

Yes, kind of a nightmare dealing with the branching alone.
22. Complex numbers confusion (how they got this expression in orange to become -1)

Or, to be pedantic, use that the Complexes can be seen as a field extension by ## x^2+ 1 ##. Then, in the extension ## \mathbb R[x]/(x^2 +1) ; x^2 +1 =0 ## You designate this new element by ##i ##..
23. Random Thoughts part 6

Every tab everything working except YouTube. I was searching for SysInternals. Which I never had??
24. Collection of Lame Jokes

If at first you don't succeed, don't try skydiving.
25. Proving eigenvalues of a 2 x 2 square matrix

Eigenvalues ##\lambda## for a matrix ##A##are defined to satisfy ##Det(A-\lambda I)=0##. This comes from ##Ax=\lambda x ##, so that ##(A-\lambda I )x=0 ##.

34. Baffled by old school exam

But it was an _open_ exam. ;).
35. I Why isn't this a Lie group?

One result I remember is that given ##G## a Lie Group; here ## \mathbb T^2##, a subset is a Lie Group if it's both a subgroup and topologically closed in ##G##.
36. B Are there two kinds of inverse with respect to closure?

Nor would it be onto, if we consider ##\mathbb N =\{1,2,..\} ##, as nothing would hit ##1##.
37. Baffled by old school exam

Worse comes to worse, time is running out on the exam, cube both sides. Only one term will remain to a non-unity power p/q. Leave it alone in one side and raise both sides to the qth power. Hardly elegant, but at least you'll get some credit. Edit: In this exercise, you first cube both sides...
38. Collection of Lame Jokes

Had to correct my friend . I told him to put a potato in his bathing suit at the beach to help him impress women. But In the front, not in the back, as he did last time.
39. Collection of Lame Jokes

Winner gets a Lapp dance.
40. Is it possible to find a number x such that 5 < x < 1?

You mean as in using Order Statistics? Say horse number five finished the race before horse number 1( of course, numbers were given before the race)?
41. Collection of Lame Jokes

That's music to Meir.
42. Collection of Lame Jokes

Weird exchange: I have something in my ear Well, it can't be Golda, she's been dead for a while.
43. Is it possible to find a number x such that 5 < x < 1?

So, the expression 5 < 1 by itself does not provide enough information to determine what this '<' means, nor how it works by itself.
44. Is it possible to find a number x such that 5 < x < 1?

Still, to keep some standards, we need to deal with Mathematical issues: What requirements must an ordering satisfy?
45. Is it possible to find a number x such that 5 < x < 1?

This works, but needs rescaling to fit the OP: Assume there are numbers S between 0 and 1. Then since the set is bounded, it has a least upper bound L, so that: 0<L<1 Now multiply thtough by L: 0< L^2<L Then L^2 is a bound lower than L. Contradiction.
46. Random Thoughts part 6

Not too confident about an organization called the " Feil" organization.
47. Collection of Lame Jokes

A club sandwich?
48. Collection of Lame Jokes

I think Turkey in Turkish is 'Gindi'
49. Collection of Lame Jokes

Abraham includes Pastrami
50. Collection of Lame Jokes

Geography, religion and meats: Turkey: Ottoman Empire, Ham: Muslims Bacon: Britain ( Roger). Rotisserie: 15:3.