5
votes
Accepted
Does $\omega$-consistency depend on the encoding?
This is a great question! In general, "reasonably strong" theories will always have distinguished implementations (the jargon is actually interpretations, but meh) of the natural numbers, ...
- 236k
2
votes
Why doesn't $x^0$ equal the same thing as $x\cdot0$?
multiplying exponents with the same base, is the same as adding the exponents, i.e. $a^b * a^c = a^{(b+c)}$
using this consider:
$$
x^0 = x^{-1} x^1 = \frac{1}{x^1}x^1 = 1
$$
OR
$$
x^3 = x^2x \\
x^2 = ...
- 51
1
vote
Modulus with negative number
We generally say that $a \equiv b \mod m$ if $a - b$ is a whole multiple of $m$. This is true for any integer $a$ and $b$, whether positive or negative.
So then $-1 \equiv 14 \mod 5$, because $-1 - 14 ...
- 21.2k
1
vote
Can you add a scalar to a matrix?
The broadcasting operator . in Julia modifies an operation or a function so that it can be expanded for matrices. For a matrix A and a scalar b, A .+ b is the matrix in which b is added to each ...
- 11
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