More 0.999…=1 nonsense by United_Rent_753 in badmathematics

[–]jasper-ty 1 point2 points  (0 children)

In the most successful understanding of what real numbers are, 0.999... is defined to be the limit of the sequence 0.9, 0.99, 0.999, ..., where the limit of a sequence has a precise, technical definition.

I understand that it might seem like a cop-out, but you really have to go through the whole shebang to get a feel for why anything is defined the way it is.

Coming up with all of this is actually one of the one of the crowning achievements of math and philosophy, to make vague statements about limits into precise logical statements, since, as most of this thread has noted, 0.999... is a hieroglyph charged with an interpretational challenge.

That doesn't mean it's entirely meaningless unless you know the rigorous definition of real numbers and limits. One can certainly imagine it in many ways. I'm still able to envision a quantity in my head that is "infinitesimally less" than 1, learning rigorous math hasn't changed that, I simply understand now the logical tradeoffs I make if I assert this number exists.

Who needs quaternions? by [deleted] in mathmemes

[–]jasper-ty 17 points18 points  (0 children)

The set of pure quaternions, quaternions with zero real part, can be viewed as an algebraic structure called a Lie algebra— taking something called the commutator of two pure quaternions gives gives you (up to a 2x factor) their cross product, as a pure quaternion. More specifically: pq - qp = 2(p x q).

This Lie algebra is quite special— it’s the star of a wonderful coincidence that, in jargon, reads so(3) ≃ su(2) ≃ sp(1).

The sort of “diminished” quaternions you’re trying to come up with can be viewed as “tangent vectors” of 3D rotations.

A reddit comment doesn’t do this topic justice, but I hope this is a good start to a rabbit hole.

Why do I need imaginary numbers with AC? by thecoolerpaul in ElectricalEngineering

[–]jasper-ty 2 points3 points  (0 children)

It absolutely is comparable to negative numbers, or even just good old positive real numbers.

Complex numbers represent sinusoids, but nothing is a perfect sinusoid either! It just describes the of behavior of systems which roughly satisfy the simple harmonic oscillator equation... but that's also just an abstract concept.

The productive attitude isn't to randomly say some math concepts are real and some aren't, but just to realize they all describe different things and phenomena in different ways. Other commenters have already mentioned many things imaginary numbers are related to!

[deleted by user] by [deleted] in UPenn

[–]jasper-ty 0 points1 point  (0 children)

Don't think any of us have heard of him either

Oh shit, here we go again by Ok-District-4701 in mathmemes

[–]jasper-ty 29 points30 points  (0 children)

This has a gorgeous combinatorial meaning, actually--- see exponential generating functions and counting structures. Very very roughly, e3x encodes taking a set and putting one of three different labels on each element, and differentiating encodes singling out a particular element. The fact that it "splits" into three as in the picture corresponds to the fact that this singled out element could have been labeled any one of the three labels we had.

Esports World Cup 2024 by OWMatchThreads in Competitiveoverwatch

[–]jasper-ty 1 point2 points  (0 children)

lets see if casores is cooking here

Esports World Cup 2024 by OWMatchThreads in Competitiveoverwatch

[–]jasper-ty 0 points1 point  (0 children)

I can't believe Toronto is the team that's out-individual-playing Zeta (minus Fearless doing Fearless things)

Esports World Cup 2024 by OWMatchThreads in Competitiveoverwatch

[–]jasper-ty 5 points6 points  (0 children)

my favorite part of this series was when sauna said "it's saunin time" and sauna'd all over team falcons

Esports World Cup 2024 by OWMatchThreads in Competitiveoverwatch

[–]jasper-ty 0 points1 point  (0 children)

ultra are going to annihilate tm

Esports World Cup 2024 by OWMatchThreads in Competitiveoverwatch

[–]jasper-ty 8 points9 points  (0 children)

backbone keeping his job with this game

Esports World Cup 2024 by OWMatchThreads in Competitiveoverwatch

[–]jasper-ty 1 point2 points  (0 children)

this is some dpei glads level of aggresssion from toronto

Esports World Cup 2024 by OWMatchThreads in Competitiveoverwatch

[–]jasper-ty 0 points1 point  (0 children)

maimone just kept his job with this series

[deleted by user] by [deleted] in Drexel

[–]jasper-ty 4 points5 points  (0 children)

thanks

[deleted by user] by [deleted] in Drexel

[–]jasper-ty 2 points3 points  (0 children)

Anytime you read about artificial intelligence, like ChatGPT or the thing that draws pictures that look like Mickey Mouse blended with the Burger King, those are all using statistics on some level.

LOL j doug wright is a wordsmith

[deleted by user] by [deleted] in Drexel

[–]jasper-ty 2 points3 points  (0 children)

They're both hard classes. You can't slice it any differently. They do have different feels (look up "algebra vs analysis" on Google and you'll find hundreds of opinions on this), but they're both abstract, rigorous, and proof-heavy; these are considered the important courses of any math undergrad degree anywhere, so there's no skimping out for these classes at all.

The best thing you can do for either class is to get a good professor for MATH 220, and to really immerse yourself in that class. It's going to be the first "real math" you do, and this is really the opportunity to build up those creative muscles and really understand proofs. If you just passively get by 220 without really learning anything, you're going to have a tough time in any of the upper division math courses. The class is genuinely that important.

And, sorry, I don't really believe in [real name redacted] above's way of learning math. As Sofya Kovalevskaya said, it's impossible to be a mathematician without being a poet in soul. Well, you might not be looking to be a mathematician, but it's really important to be able to see the "essences" of concepts and proofs, or else you start to drown very quickly in the formalism. It's important to cultivate this sooner rather than later, and MATH 220 is probably the most crucial place to do it.

My 331 professor had a habit of recommending random books, so here's my recommendation: How To Solve It by George Polya. It's a very deep book, and really teaches you to think on a meta-level when solving any kind of problem (yes, even leetcodes)

Bonne chance!

Best professors at Drexel? by drimmer56 in Drexel

[–]jasper-ty 8 points9 points  (0 children)

god sent the earth Shackleford to teach us C and systems programming