Expert Help & Insights for Discrete Mathematics Answers

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Prove that $⋂_{x \in [- 1, 0]} [x, 1 + x] = {0}$
Answer:
So my approach is a little bit different than the usual, that ${0} \subset ⋂_{x \in [- 1, 0]} [x, 1 + x]$ and that $⋂_{x \in [- 1, 0]} [x, 1 + x] \subset 0$ .
So I tried to do it that we have $a \in [x, 1 + x],$ , $x \in [- 1, 0] ⟹ a \in [- 1, 1]$ , and is a real number.
So now if we look at $x = - 1 + ϵ$ , where $ϵ > 0$ and is a small real number, we have some $a_{0} \in [- 1 + ϵ, ϵ]$ and if we look at $x = - ϵ$ , we have $a_{1} \in [- ϵ, 1 - ϵ]$ .
Ok, so what I want to show is that if $a_{1}, a_{0} \in ⋂_{x \in [- 1, 0]} [x, 1 + x]$ iff $a_{1} = a_{0}$ .
Now if we look at the inequalities (we say that ${a \in R | \forall x \in [- 1, 0] : a \in ⋂ [x, 1 + x]}$ ):
$- 1 + ϵ \leq a \leq ϵ \land - ϵ \leq a \leq 1 - ϵ$
$- ϵ \leq a \leq ϵ$
and as $ϵ \to 0$ , we get: $0 \leq a \leq 0 ⟹ a = 0 = a_{1} = a_{0}$
Is my proof correct? How would you show it the usual way (with subset going both ways)?

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This subject is called Discrete mathematics.
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Dealing with discrete Math is an interesting subject because discrete Math equations can be encountered basically anywhere from scheduling of sports games and live shows to education where each person is examined online. It is a reason why discrete math questions that we have collected for you are aimed at solutions that go beyond equations to provide you with the answers that will help you understand the concept. Still, discrete Math equations are explained as well by turning to problems in computer science, programming, software, and cryptography among other interesting subjects like software and mobile apps development.

Discrete math