Translation for $if \exists i \in [m]$ s.t. $x_i = x$

Question

I am trying to read a book on machine learning which define the error function $hS(x)$ where $$[m] = \{1,\ldots,m\}$$ as being

equation

However I do not understand well basics math notation, would you mind helping me to understand this one, and also if you have some documents available in order to learn the language.

Thanks!

score 1 · Accepted Answer · answered Jun 21 '17 at 20:08

1

This is saying in English: "if there exist an $i$ in the set $[m]$ such that $x_i = x$, then $hS(x) = y_i$. Otherwise, $hS(x) = 0$."

answered Jun 21 '17 at 20:08

AsafHaas

769

score 1 · Answer 2 · answered Jun 21 '17 at 20:19

1

Here's how I would have written it:

We define the function $hS$ by mapping $x_i \mapsto y_i$ (read "mapping $x_i$ to $y_i$") for $i \in [m]$ and all other inputs to $0$.

What this means is, $hS$ takes a value $x$ as input. If that value $x$ happens to be equal to $x_1$ then $hS(x) = hS(x_1) = y_1$; if that value happens to be equal to $x_2$ then $hS(x) = hS(x_2) = y_2$; and in general, if $x = x_i$ then $hS(x_i) = y_i$. Finally, if $x$ is not equal to $x_1$ nor $x_2$ nor $x_3$, . . ., nor $x_m$ then $hS(x) = 0$.

answered Jun 21 '17 at 20:19

Trevor Gunn

27,041

what s.t means specifically also? – matel Jun 21 '17 at 20:40
@matel It is an abbreviation for "such that". AsafHass provided a direct translation in his answer. – Trevor Gunn Jun 21 '17 at 20:50

Translation for $if \exists i \in [m]$ s.t. $x_i = x$

2 Answers2