English to Quantifier every real number

37 Views Asked by At

how to write this statement

"every real number is not greater than six"

in symbols (quantifiers)

2

There are 2 best solutions below

1
On

The symbol for "for every, for each, for all, for any" is $\forall$. Now, we can write

$$ \forall x: x \not > 6 $$

But can we clean this up? Ah, yes we can. If a real number is not greater than 6, then what? It must be less than or equal to 6. So we may then write

$$ \forall x: x \leq 6$$

and move on.

1
On

Are you asking how to write it in stack exchange or just in general? If the former, there are several good posts in stack exchange that go over how to format here. A simple google search of something like "how to format questions in math stack exchange" or something like that should bring them up. If it is the latter, you'd write $\forall x \in \Bbb R, x \ngtr 6$