Commented Nov 9, 2024 at 4:17 $\begingroup$ Implicit vs. explicit is not about having a matrix form or not, it is about having to solve an equation for the new values or not. $\endgroup$ – PierreCarre

2018年4月7日 · I was asked to find a CW complex for the Möbius strip with one 0-cell, two 1-cells, and one 2-cell. I can find a CW complex for a Möbius strip with more cells (two 0-cells, three 1-cells and a sin...

2019年2月25日 · The problem is that most of first-order mathematical theories have more than one model; in particular, this happens for $\mathsf {PA}$ and related systems (to which Gödel's (First) Incompleteness Theorem applies).

2017年1月14日 · It is just a short notation to make good use of limited display and storage space. The used string in base 10 representation, called exponential or scientific notation, and the encoded rational number are related by $$ (\underbrace{\pm d.ddd\cdots d}_{\mbox{mantissa }m} \,\,\, \mbox{E}\underbrace{\pm dd\cdots d}_{\mbox{exponent }k})_{10} = m \cdot 10^k $$

Commented Oct 8, 2015 at 17:26 $\begingroup$ I would say that this exactly addresses the question. As a software engineer, this means that the algorithm is nondeterministic (assuming the random number generators are not seeded with the same value), and you cannot rely on the answers being the same from run to run. $\endgroup$

I am trying to understand the Poincare Disk model of a hyperbolic geometry and how to measure distances ...

However, the relationship between the common geometry and the geometry of vector spaces is that of a model and an abstract theory. The above vector identity does not prove the Pythagorean theorem. It only shows that there is a tight relation between the model and the theory.

2015年5月11日 · ├── Complete Segal Spaces │ ├── [BC, 10 Pages] Equivariant Complete Segal Spaces.pdf │ ├── [Brito, 26 Pages] Segal Objects and the Grothendieck Construction.pdf │ ├── [Rasekh, 17 Pages] A Model for the Higher Category of Higher Categories.pdf │ ├── [Rasekh, 44 Pages] Complete Segal Objects.pdf ...

2019年4月23日 · The whole scenario ignores you, and assumes that you have none left over. If you take a fair share instead, then you are dividing it by a number one greater. To model division by zero in that case, even you yourself would disappear, and so would the remaining apples. Where did they go? $\endgroup$ –

2019年12月20日 · You should use $$\sum_{i=1}^n x_i y_i = a\sum_{i=1}^n x_i^2 +b\sum_{i=1}^nx_i^3$$ $$\sum_{i=1}^n x_i^2 y_i = a\sum_{i=1}^n x_i^3 +b\sum_{i=1}^nx_i^4$$