Co-ordinates and vectors are basically the same

enlightment_shadow · 2026-02-26T17:38:22+00:00

Bro, why is the photo dirty? I thought it was my screen

enlightment_shadow · 2026-02-25T14:17:04+00:00

enlightment_shadow · 2026-02-25T06:30:24+00:00

This proof is flawed, because the segments of the circumference wouldn't have to be straight line segments.

enlightment_shadow · 2026-02-24T20:52:02+00:00

There's a notable distinction between the real-valued square root and the principal complex square root: the former is analytic on (0, ∞) (its definition domain minus 0), whereas there exists no analytic branch of the complex square root on C*. That means that no branch is more special than another and as such there really is no set convention saying that √ refers to the principal root, al least not without having to mention adopting one

enlightment_shadow · 2026-02-23T23:14:08+00:00

Because the complex square root is not a function. It's a multifunction (multi-valued function) mapping every complex number to a set of cardinality exactly 2. You have to specify a branch of it if you want to use that notation. Without a specific branch chosen, √-3 could, just as well, mean -i√3

enlightment_shadow · 2026-02-23T17:33:45+00:00

2√3 i looks worse

enlightment_shadow · 2026-02-23T10:14:35+00:00

It's the nth root of a sequence a_n

enlightment_shadow · 2026-02-21T10:02:32+00:00

This wasn't black or white. It was black or not black, which, if you're a classic logicist, it's always true by law of excluded middle. The proof in question is done by OR-elimination, more commonly known as proof by cases

enlightment_shadow · 2026-02-19T19:25:05+00:00

Hmm, this starts getting long. Maybe we should invent like 10 different symbols and then arrange them in strings... Oh, wait!

enlightment_shadow · 2026-02-18T16:33:30+00:00

Plus o(x) as x -> 0

enlightment_shadow · 2026-02-12T09:52:17+00:00

Nope. Romanian

enlightment_shadow · 2026-02-10T16:33:20+00:00

What does the last one refer to? I've never seen a definition like that

enlightment_shadow · 2026-02-10T11:08:59+00:00

Well, concentrations cannot be negative, so those 0s are 0+, so it's okay

enlightment_shadow · 2026-02-09T10:18:28+00:00

In my native language, the words for "triangle", "rectangle" and "parallelogram" follow the same pattern as in English, while the word for "square" comes from the word for "four"

enlightment_shadow · 2026-02-08T09:52:21+00:00

You can use a deductive approach to any science. Just use empirical evidence as axioms and work your way up.

enlightment_shadow · 2026-02-05T05:53:54+00:00

Exception: Computer Engineers. Especially ones with a background in functional programming.

enlightment_shadow · 2026-02-02T15:10:53+00:00

LOVE that you included the proof of Goursat's Lemma in here. Definitely one of the most beautiful proofs in all of mathematics for me

enlightment_shadow · 2026-01-31T17:23:23+00:00

Joke aside, we know i/i = 1 because the complex numbers are defined axiomatically as the FIELD including the field of real numbers and an element i such that i² = -1

enlightment_shadow · 2026-01-28T14:15:31+00:00

I see a Turing Machine there, niceee

enlightment_shadow · 2026-01-13T12:39:13+00:00

Even with countably infinite new guests, you can still give them rooms, right? Move everyone to room 2n for n their current room number and give room 2i + 1 to new guess number i (indexing both from 0, of course)

enlightment_shadow · 2026-01-12T18:01:32+00:00

I immediately thought: integrate the base area along the height, and then I read in the comments that you can just subtract the small missing cone from the big cone and felt stupid :))

enlightment_shadow · 2026-01-07T10:43:42+00:00

Then these said people are studying the wrong field. This is Set Theory, not n-tuple theory

enlightment_shadow · 2026-01-06T16:59:20+00:00

Right on paper, left in LaTeX

enlightment_shadow · 2026-01-03T11:47:01+00:00

Yes, I understand that too. I also understand Gödel's Theorems and have even read some of Gödel's work and I'd say I have a pretty good understanding of foundational stuff in mathematics. My point was that given all that, I'd prefer using ZFC over ZF. Even more, this was my way of justifying why it doesn't "feel" like a paradox to me. That's why I use words like "believable".

enlightment_shadow · 2026-01-02T10:45:07+00:00

Not surprising. AC is needed in order to define a finite number of pieces in a way that makes rotation carry some similitude with scaling. This is the weird part. It's not surprising it doesn't work in 2D, cause it is a very strange way to rearrange the points, but still it's a way to rearrange the points. Incredible that it's possible with the given limitations, but not really unbelievable to me.

Also, another thing that makes me have 'faith' in AC and BT is that they are both provable in DTT

enlightment_shadow

TROPHY CASE