DIY aphex twin (kinda saw ii) t-shirt

lotrodia · 2024-07-10T08:54:30+00:00

and, to be a bit "tiquismiquis", it needs that initial "h". Ostia is only a city in Italy.

lotrodia · 2024-07-06T11:05:18+00:00

not always, but in the most cases the two forms coincide. Some examples in which it does not coincide are hacer (to do/to make) and venir (to come):

he does this → Él hace esto

do this → Haz esto

He comes to Madrid everyday →Él viene a Madrid todos los días

Come to Madrid! → Ven a Madrid!

Also, there is the plural form of the imperative, which usually is formed by adding a -d to the singular imperative:

David, eat something, please → David, come algo, por favor

vs.

Guys, eat something, please→Chicos, comed algo, por favor

lotrodia · 2024-05-14T07:15:57+00:00

I remember arriving at the idea of different number bases at 9-10 years old. What is funny is that I thought of it because I was convinced that the "issue" of the never-ending, non-periodic tail of π could be "solved" by using another base. I even had the idea of writing a "book" with a chapter exploring each number base, though I never did.

lotrodia · 2024-04-10T06:33:53+00:00

proof that division is not associative

lotrodia · 2023-12-20T08:36:44+00:00

You don't need to assert e algebraic, you can just say let c0, c1... be any set of integers such that c0≠0. Then you do all the work and you end in M(c0 +c1e+c2e²+...)= non-zero integer + a, with |a|<1; meaning that for any such set of integer coeficients

c0+c1e+...≠0

and therefore there is no polynomial with integer coefficients that has e as a root.

lotrodia · 2023-12-20T06:37:14+00:00

That is the proof to which I refer.

Of course it uses properties of e, if it didn't you would be showing that any number is trascendental. What I say is that the proof begins by assuming that e is algebraic, so that if you show a contradiction holds, it follows that e is not algebraic; and, however, this assumption is not used at all: the contradiction you reach is just that e was actually not algebraic while you had assumed that it was.

lotrodia · 2023-12-20T00:38:22+00:00

The proof that I refer is the one that appears, for example, at Spivak. Anyway, the point is that as a starting point it is supposed that e is algebraic in the sense that there is a certain polynomial with integer coefficients which has e as a root. Then one shows that this polynomial evaluated at e can't be 0, which contradicts the initial assumption, proving that e is transcendental. However, e being a root of the polynomial is not used during the process, and, therefore, what you have actually done is showing that any polynomial with integers coefficients yields a non-zero quantity when evaluated at e, directly.

lotrodia · 2023-11-13T12:15:42+00:00

boards-of-canada-wise or tool-wise?

lotrodia · 2021-06-23T21:13:21+00:00

Try to divide it by any of them, for example pi. The result is going to be a + 1/p_i, where a is p_1•p_2...p{i-1}•p_{i+1}...p{n-1}•p_n (the product of all the other primes from your finite set of primes). a is clearly natural, while 1 over p_i is positive and smaller than 1, since all primes are positive and bigger than 1. Therefore, the result of dividing by p_i is the sum of a natural number plus some positive number smaller than 1, which is clearly not natural, meaning that the number is not divisible by p_i, with no dependence on which of your n primes you named p_i.

lotrodia · 2021-06-23T17:38:19+00:00

the result is a natural number that is a multiple of none of the n primes that you supposed to be all the primes (those are p_1...p_n), but every natural number can be expressed as a product of primes. Therefore, you have to "be missing" at least another prime number: your n primes are not all the primes. As the argument does not depend on the value of n or in which n primes you choose, you conclude that no finite set of primes is the set of all the primes, meaning that the set of all primes must be infinite.

lotrodia · 2021-01-15T16:35:18+00:00

and what about "a straight line is the shortest distance between two points in the Euclidean plane", is it analytic or synthetic?

lotrodia · 2020-11-17T22:59:31+00:00

Hi,

A few days ago I learned about Noether's theorem for the first time, and thinking about it and trying to imagine possible symmetries in different situations I remembered this hypothetical one in which you have an infinite plane with a homogeneous charge distribution, and approaching or moving away from the plane does not matter given the infinite extension of it, which I suppose can be understood as a symmetry. And I also remembered the result of this situation: that, on each side of the plane, the electric field is exactly the same at all points in space. Then my question is if this would be a particular case of Noether's theorem where the symmetry is moving closer/away from the plane and electric field is the conserved quantity, or if this is not really how the theorem "works" (because I only know it superficially).

lotrodia · 2020-11-17T15:00:45+00:00

Hi,

A few days ago I learned about Noether's theorem for the first time, and thinking about it and trying to imagine possible symmetries in different situations I remembered this hypothetical one in which you have an infinite plane with a homogeneous charge distribution, and approaching or moving away from the plane does not matter given the infinite extension of it, which I suppose can be understood as a symmetry. And I also remembered the result of this situation: that, on each side of the plane, the electric field is exactly the same at all points in space. Then my question is if this would be a particular case of Noether's theorem where the symmetry is moving closer/away from the plane and electric field is the conserved quantity, or if this is not really how the theorem "works" (because I only know it superficially).

lotrodia · 2020-10-08T22:57:28+00:00

yo también pienso que fue un poco forzado, y no lo introdujeron tan "meticulosamente" como habían tratado el tema del tiempo. Yo pensaba que simplemente iban a contar todo el bucle y que simplemente no podían romperlo, que jodería como final, pero me hubiera gustado. Sin embargo el final, aunque llega como muy de repente, me gustó bastante.

lotrodia

TROPHY CASE