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How can I specify within a formula that the inserted values for different variables may only vary between $0$ and $1$?

Example: $x = y + z$, where the values used for $y$ and $z$ may take on any value between $0$ and $1$, but not outside this range.

I am looking for the mathematically correct notation for this. Probably one must make a case distinction here, but I am very unsure how to write this down.

DMcMor
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john
  • 23

2 Answers2

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This is presuming that $y$ and $z$ are real numbers. You may specify it like this:

$$x = y + z$$ $$ y, z \in [0,1]$$

the LaTeX command is backslash in: \in. It reads "is an element of". Those brackets are not arbitrary. the square bracket, '[' means "0 is included". The other one ']' means "1 is included". If you wanted to exclude either edge case you use round brackets: $ x = y+ z$, where $y, z \in (0,1]$ means "between 0 and 1 without 0 but including 1"

Michael Stachowsky
  • 2,943
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There are a lot of different ways to do this. Here are a few options, but it's really a matter of taste.

  1. $$x = y + z,\quad 0\le y,z\le1$$
  2. \begin{align*} x &= y+z\\ 0 &\le y,z \le 1 \end{align*}
  3. \begin{align*} x &= y+z\\ 0&\le y \le 1\\ 0 &\le z\le 1 \end{align*}
  4. $$x = y+z,\quad y,z\in [0,1]$$
DMcMor
  • 9,407