Physics Forum » General Math
by Pikkugnome
5h ago
Digits of an uncomputable number, as I understand, can't be produced. However all real numbers have rational approximations. Does it mean that there exists a bound for the rational approximation. It is odd to talk about rational approximations in a non-contructive sense, but I am ok with it. I... Read more ..read more
Physics Forum » General Math
by bland
5h ago
I just saw that one of the ways of calculating Pi uses the set of prime numbers. This must sound crazy even to people who understand it, is it possible that this can be explained in terms that I, a mere mortal can understand or it is out of reach for non mathematicians ..read more
Physics Forum » General Math
by Heisenberg7
19h ago
I can't decide which one is better to use. I know for a fact that the second one is correct, but I would like to know if I can use the first one too. Which one would you use? $$\forall x \in \mathbb{Z} (\exists y \in \mathbb{Z} : x > y)$$ Or $$\forall x \in \mathbb{Z} (\exists y \in \mathbb{Z}... Read more ..read more Physics Forum » General Math by Agent Smith 1d ago The above was part of a conversation on ##\pi## and the implication seems to be that the more accurate the value of ##\pi## in our calculations in an engineering context, the more circular our construction. Questions: 1. Is this true? More accurate values of ##\pi## allow... Read more ..read more Physics Forum » General Math by logicgate 3d ago As I understand, a ratio is a comparison between two or more quantities. Ratios involve two or more numbers. Whereas a fraction is a single real number. Why are ratios and fractions the same when ratios involve two or more different numbers whereas fractions represent only ONE real number like... Read more ..read more Physics Forum » General Math by Agent Smith 4d ago As a high school student we were told to use ##\frac{22}{7}## as a rational approximation for ##\pi##. However, to the same level of accuracy, ##\frac{314}{100} = \frac{157}{50}## is also ##\pi## and since there's a ##100## and a ##5## in the denominator many calculations would've been far... Read more ..read more Physics Forum » General Math by scjiang 5d ago I have been attempting a question about noisy linear dynamical systems lately. Specifically, suppose we are given a linear dynamical system$$ x_t = Ax_{t - 1} + \mathcal{N}(0, \sigma^2)  where $A$ is orthogonal, $x_t \in \mathbb{R}^n$, and $\mathcal{N}(0, \sigma^2)$ is a normal distribution... Read more ..read more
Physics Forum » General Math
by Astronuc
1w ago
group of nine mathematicians has proved the geometric Langlands conjecture, a key component of one of the most sweeping paradigms in modern mathematics. The proof represents the culmination of three decades of effort, said Peter Scholze, a prominent mathematician at the Max Planck... Read more ..read more
Physics Forum » General Math
by Agent Smith
1w ago
Vide supra is a first few stages of Pascal's Triangle. The numbers themselves are the coefficients for the binomial expansion of ##(a + b)^n##, where ##n \in \{0, 1, 2, ... \}##. I'm just curious whether each stage has a special meaning, unique to it. My lack of knowledge... Read more ..read more
Physics Forum » General Math
by Heisenberg7
1w ago
I've seen a lot of people use implication and equivalence logic incorrectly. For example, when solving equations (i.e. ##x - 2 = 3 \implies x = 5##). Implication is not reversible, thus it only works in one way. By saying, ##x - 2 = 3 \implies x = 5##, you are essentially saying that it is... Read more ..read more

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