Timeline for Prove that If $a$ and $b$ are real numbers with $a < b < 0$ then $a^2 > b^2$

9 events

when toggle format	what		by	license	comment
Jul 17, 2019 at 13:09	comment	added	José Carlos Santos		Yes. I often tell to my students to simply write $\implies$ instead of $\iff$ whenever $\implies$ is enough, in order to decrease the possibility of an oversight. But it is correct in this case.
Jul 17, 2019 at 13:07	comment	added	Stokolos Ilya		One more question: $ (1)⟺ (2) ⟺(3) ⟺(4)$ Would that be correct in our scenario?
Jul 17, 2019 at 13:01	comment	added	José Carlos Santos		One possibility would be eliminate the sentence “Given that $a<b<0$” and to add, after your sequence of assertions “Since we are assuming that $(1)$ holds and since $(1)\implies(2)\implies(3)\implies(4)$, this proves that $a^2>b^2$”.
Jul 17, 2019 at 12:56	comment	added	Stokolos Ilya		If I am to choose the second option, how am I supposed to do it properly?
Jul 17, 2019 at 12:56	comment	added	José Carlos Santos		Either you do show explicitely a link between them, as I did, or you assert explicitely that each assertion follows from the previous one.
Jul 17, 2019 at 12:54	comment	added	Stokolos Ilya		Do you need to explicitly show that there is a link between them? I've numbered each step, assuming that it is evident that each step follows from the previous one.
Jul 17, 2019 at 12:52	vote	accept	Stokolos Ilya
Jul 17, 2019 at 12:48	history	edited	José Carlos Santos	CC BY-SA 4.0	Typographical improvement
Jul 17, 2019 at 12:42	history	answered	José Carlos Santos	CC BY-SA 4.0