0
$\begingroup$

This might be a silly question, but I have no clue what it means:

enter image description here

it's from this question i'm working on:

enter image description here

I'm taking a CS course, and all the math i've done is calculus and linear algebra. I've never see approximation squiggly lines with a subscript. What on earth? I wish schools prepared us more properly, before throwing us the wolves. Half the time I'm spending trying to decipher what any of this means mathematically.

$\endgroup$
1
$\begingroup$

The text you quote defines exactly what $a \approx_f b$ means: $a \approx_f b$ if and only if $f(a) = f(b)$. For example, if we let $g: \mathbb R \rightarrow \mathbb R$ be defined by $g(x) = x^2$, then $2 \approx_g -2$ because $g(2) = 4 = g(-2)$, but it is not the case that $1 \approx_g 2$, because $g(1) = 1$ and $g(2) = 4$.

$\endgroup$
6
$\begingroup$

The passage you have there defines $\approx_f$ to be a certain relation. For any $x$ and $y$, $x \approx_f y$ is either true or false. The passage gives a definition for exactly when it is true.

In other words, it doesn't mean anything in particular outside this passage. This passage defines it.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.