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**courteous** **1)** "Prove $\displaystyle A\cap{A}=A\cup{A}=A$." (This is very first workbook exercise for our Real (and Complex) analysis.)

I have more: **2)** "Prove that if $\displaystyle a>b\Rightarrow -a<-b$" and prove that **3)** "square of every negative number is a positive number".

I presume that the more elementary it is, the harder it is (like *Principia *proving that 1+1=2 (after how many pages?(Speechless)))?

How many ways can such be proven (I think we've done it in discrete math(Thinking), but workbook is from analysis)?