5 votes

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, ...
Noah Schweber's user avatar
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 = ...
oatmeal's user avatar
  • 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 ...
ConMan's user avatar
  • 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 ...
ullahmukhtar's user avatar

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