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I am reading "Real Analysis: Foundations and Functions of One Variable"by Miklos Laczkovich and Vera Sos ...
I need help with an aspect of Example 10.7 (2) ... Example 10.7 (2) reads as follows:View attachment 7252
In the above text, we read the following: "... ... Since whenever $$\lvert x - 2 \lvert \lt \frac{1}{2} , \lvert x - 1 \lvert \gt \frac{1}{2}$$ ... ... "Can someone please explain why:$$\lvert x - 2 \lvert \lt \frac{1}{2} \Longrightarrow \lvert x - 1 \lvert \gt \frac{1}{2}$$ ...Help will be appreciated ... Peter
I need help with an aspect of Example 10.7 (2) ... Example 10.7 (2) reads as follows:View attachment 7252
In the above text, we read the following: "... ... Since whenever $$\lvert x - 2 \lvert \lt \frac{1}{2} , \lvert x - 1 \lvert \gt \frac{1}{2}$$ ... ... "Can someone please explain why:$$\lvert x - 2 \lvert \lt \frac{1}{2} \Longrightarrow \lvert x - 1 \lvert \gt \frac{1}{2}$$ ...Help will be appreciated ... Peter