Mathematical Notation.......

Question

$x$ and $y$ are two different, positive and real numbers. How can you denote this using mathematical symbols for positive and real numbers.

I searched on google but didnot get a reliable answer. Please help me. Thanks in advance.

Answer 1

First you need to settle on a symbol for real numbers. I personally prefer $\mathbb R$, but you might find $\textbf R$ occasionally. Having made that choice, it's a simple matter to append a superscript plus sign to that symbol.

Believe it or not, some people consider 0 to be a positive number, then what I consider positive numbers they consider "strictly positive" numbers. It wouldn't hurt to be clear where you stand on this.

Then to say that $x$ and $y$ are distinct numbers drawn from this set, you could write $0 < x < y$ (or $0 \leq x < y$ for the positive zero weirdos). The problem with this is that it precludes the possibility that $y < x$. Better then to write $x \neq y$ if you don't require one to be larger than the other, merely distinct.

Therefore,

$x, y \in \mathbb R^+$, $x \neq y$.

is the best way to go about it, in my opinion. Make sure to state in words what $\mathbb R^+$ stands for at some point.

Answer 2

1. $x\neq y\in \mathbb{R}_+$
2. $x,y\in\mathbb{R}_+, x\neq y$
3. Since $\mathbb{R}$ is totally ordered, we have trichotomy so we can say $0 < x < y \in \Bbb{R}$

There are many more ways you can do this.