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### 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, ...

### 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 = ...
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 ...
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 ...

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