How to write this statement in mathematical notation? No integer bigger than 70 can be expressed as a sum of 3 integers smaller than 30
My attempt:
$U_1 = {x∈Z∶x>70 }$
$U_2 = {y∈Z∶y<30 }$
$∄x ∈ U_1 , ∀y ∈ U_2  , x = y_1+y_2+y_3$
I understand that there are many ways to write a sentence in mathematical notations, just wondering whether there is an easier way to write this? Thanks guys :)
 A: Just
$$\nexists a,b,c\in\Bbb Z: (a+b+c>70)\land(a,b,c<30)$$
Anyway the statement isn't true, I dont understand why you want to write this.
A: The first step would be to try to rewrite your sentence using the expressions "There is", "There is no", "which is",  "which satisfies", etc..., since these are directly translatable to a formal language: "There is=$\exists$", "There is no"=$\not\exists$; For "which satisfies some property", we simply write the property; and so on...
I'd rewrite your expression as: "There is no integer $x$ which is larger than 70 and for which there exist 3 integers, $y_1,y_2,y_3$, which are smaller than 30 and add up to $x$".
So simply applying the first paragraph, we translate it to:
$$\not\exists x\in\mathbb{Z}(x>70 \land(\exists y_1,y_2,y_3\in\mathbb{Z}(y_1<30\land y_2<30\land y_3<30 \land y_1+y_2+y_3=x)))$$
I prefer to use parentheses since they make it  clearer how elements "depend" on each other (in the above, $y_1,y_2$ and $y_3$ "depend" on $x$.
Note, however, that this sentence is false (e.g. $71=29+29+13$).
