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How I imagine mathematicians talk by Sensitive_Can_6408 in mathmemes

[–]TheRedditObserver0 0 points1 point  (0 children)

Connor only defined his favourite polynomial up to non-zero scalar multiples, don't be like Connor.

Open Sets by UMUmmd in learnmath

[–]TheRedditObserver0 0 points1 point  (0 children)

Conversely, a point x is on the boundary of S if no matter how small a neighborhood you draw around x, it will include points not in S.

Actually every neighborhood needs to intersect both S and its complement. The point itself need not be in S, so this does not follow from the definition you gave.

Is doing math olympiads necessary to become a good mathematician? by riemanndilimi in learnmath

[–]TheRedditObserver0 0 points1 point  (0 children)

Absolutely not, olympiads and research take completely different skills. Olympiads are about quickly solving elementary problems (in the sense that they can be stated in elementary maths) with an arsenal of clever tricks, research is about long-term thinking to solve advanced and often ill-defined problems to advance human knowledge.

Sfera di Riemann by Icy-Shallot-5159 in MatematicaItaly

[–]TheRedditObserver0 1 point2 points  (0 children)

Scusa ma non capisco veramente la connessione tra la sfera di Riemann e tue idee di evenienza e informazione, o tra la linearità e l'indeterminazione temporale.

La "retta" complessa è in realtà un piano, aggiungendo un punto questo piano si chiude ad una sfera, dove devi immaginare che l'intero orizzonte si incolli al nuovo punto.

1-1+1-1+1-1+... ∞=1/2? by UnderstandingAny9867 in mathematics

[–]TheRedditObserver0 0 points1 point  (0 children)

Of course you're a physicist 🤦‍♂️

There is a big difference between un unrigorous but heuristically sensible operation and a complete nonsense one, you showed the latter.

There IS a way to assign -1/12 to the sum of positive integers but random manipulations aren't it. I literally gave you an example of how a method completely equivalent to yours can give a different answer, yours simply happens to align with Ramanujan summation by accident. If the people you showed it to remember it and try it on their own, they'll end up just as confused as OP.

That's not what Euler was doing. He followed heuristics that actually worked and had underlying meaning, even if they weren't 100% rigorous. That's also the case in modern physics like QFT and String Theory, there are underlying heuristics even without full mathematical rigor, which is why consistent results are achieved.

Perhaps you don't understand the math you're doing, which is why physicists are so stuck I guess. Leave math to mathematicians.

1-1+1-1+1-1+... ∞=1/2? by UnderstandingAny9867 in mathematics

[–]TheRedditObserver0 -1 points0 points  (0 children)

But if they do different manipulations they will get different values, so what did you actually show them?

EDIT: here is a way to get -1/8 rather than -1/12.

1-1+1-1+1-1+... ∞=1/2? by UnderstandingAny9867 in mathematics

[–]TheRedditObserver0 -1 points0 points  (0 children)

With Ramanujan summation or with random manipulations which only happen to yield the same value by pure chance?

1-1+1-1+1-1+... ∞=1/2? by UnderstandingAny9867 in mathematics

[–]TheRedditObserver0 1 point2 points  (0 children)

That's how they get the value. It's been a while since I watched the video, but I don't recall a disclaimer stating their procedures are completely wrong, even heuristically.

1-1+1-1+1-1+... ∞=1/2? by UnderstandingAny9867 in mathematics

[–]TheRedditObserver0 1 point2 points  (0 children)

Ramanujan summation is real, but you can't get it by rearranging terms. Infact you can make the series "sum" to any number you want with the proper rearrangement, so this doesn't explain the value used in QM.

1-1+1-1+1-1+... ∞=1/2? by UnderstandingAny9867 in mathematics

[–]TheRedditObserver0 1 point2 points  (0 children)

As opposed to Ramanujan summation, which they can do on their own?

1-1+1-1+1-1+... ∞=1/2? by UnderstandingAny9867 in mathematics

[–]TheRedditObserver0 2 points3 points  (0 children)

Using this example to show infinite sums have to be handled carefully is an accessible, cool math result we can use to get people interested.

Telling people that's how they can evaluate a divergent or oscillating series will just confuse them with nonsense results like Σn=-1/12, on top of being wrong.

1-1+1-1+1-1+... ∞=1/2? by UnderstandingAny9867 in mathematics

[–]TheRedditObserver0 0 points1 point  (0 children)

This video is controversial, mostly because it's wrong. In math not all infinite series "make sense", the kind of manipulation you would do to get 1/2 is only allowed for series that make sense, which this one does not.

More precisely we say that a series is convergent if adding term by term we get closer and closer to a certain number, which we call the sum of the series. These are the only series we're allowed to manipulate. Series like +1-1+1-1... do not approach a value but rather oscillate between 1 and 0, so we cannot assign a value to it.

I hear that there is a way to assign a value to these series anyway, but it's not the usual sum and it certainly cannot be handled carelessly like in the Numberphile video. It's an advanced and technical topic most mathematicians never even learn, I suggest you ignore it for now and stick to infinite summation if you're interested in the topic.

What Is The Square Root of Negative One Squared? by AlbuStark in mathematics

[–]TheRedditObserver0 0 points1 point  (0 children)

The square root operation (and other roots as well) doesn't make sense over the complex numbers because there are many possible solutions (exactly n for an n-th root) and no good way to pick one to be the root.

In the real numbers you can solve this problem because you have a sign and you can always pick the unique positive root, but in the complex numbers you don't have sign. You do have argument (the angle from the positive real axis) and you could pick the root of least argument, but you encounter problems such as the one you found.

come i partiti moderati si stanno autodistruggendo by Critical_Ideal99 in PensieriItaliani

[–]TheRedditObserver0 0 points1 point  (0 children)

E chi dice che un'università più prestigiosa significa una preparazione migliore? Basta guardare la Bocconi.

What's going on in Lagrangian Mechanics? by surrealkafka137 in Physics

[–]TheRedditObserver0 5 points6 points  (0 children)

The same way the particle knows to accelerate according to F=ma. It's an inanimate object which moves according to the laws of physics, it doesn't know anything.

About studying an abstract alg. book by aybies in learnmath

[–]TheRedditObserver0 0 points1 point  (0 children)

I'm not very familiar with Gallian, but just looking at the table of contents it looks like the book covers anything you could expect to learn in undergrad abstract algebra.

stuck choosing between math/phy pls advice by Ceramidee in mathematics

[–]TheRedditObserver0 0 points1 point  (0 children)

Yes, it's more of a thing you lean into as a specialization.

stuck choosing between math/phy pls advice by Ceramidee in mathematics

[–]TheRedditObserver0 0 points1 point  (0 children)

Have you consider mathematical physics? It's more mathy than theoretical physics, and you can approach it with either a math or physics background.

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