- #1
operationsres
- 103
- 0
I can't understand a statement in a proof in a textbook.
I'm going to terminate the proof at the line that I don't understand.
Prove that there exists an [itex]x \in \mathbb{R}[/itex] such that x2=2.2. Their proof until line I don't understand
For this, we define [tex] S:= \{y \in \mathbb{R} : 0 \leq y^2 \leq 2\} [/tex] Since [itex]0 \in S[/itex], S is a nonempty. Further, S does not contain real numbers y≥2 since the last inequality implies that [itex]y^2 - 2 = (y-2)(y+2)+2 \geq 2[/itex] ...
3. Reason why I don't understand
In the definition of S, they say that [itex]0 \leq y^2 \leq 2[/itex]. Subtracting 2 from everything, [itex]-2 \leq y^2 - 2 \leq 0[/itex], which leads to [itex]y^2 - 2 \geq -2[/itex] ... But they've claimed that [itex]y^2 - 2 \geq 2[/itex] - why?
I'm going to terminate the proof at the line that I don't understand.
Homework Statement
Prove that there exists an [itex]x \in \mathbb{R}[/itex] such that x2=2.2. Their proof until line I don't understand
For this, we define [tex] S:= \{y \in \mathbb{R} : 0 \leq y^2 \leq 2\} [/tex] Since [itex]0 \in S[/itex], S is a nonempty. Further, S does not contain real numbers y≥2 since the last inequality implies that [itex]y^2 - 2 = (y-2)(y+2)+2 \geq 2[/itex] ...
3. Reason why I don't understand
In the definition of S, they say that [itex]0 \leq y^2 \leq 2[/itex]. Subtracting 2 from everything, [itex]-2 \leq y^2 - 2 \leq 0[/itex], which leads to [itex]y^2 - 2 \geq -2[/itex] ... But they've claimed that [itex]y^2 - 2 \geq 2[/itex] - why?