Math CentralQuandaries & Queries


Nazrul, a teacher:

We know that if a>b then (1/a)<(1/b)
But why 5> -2 implies (1/5)>(1/-2) .
Thank you in advance for your help.

It is true that a>b then (1/a)<(1/b) for for a,b > 0 or for a,b < 0. As you have shown, it is not true otherwise.
Because 5 > 0 > -2 implies (1/5) > 0 > (1/-2). All reciprocals of positive numbers are positive, all reciprocals of negative numbers are negative.

Try drawing the graph of x |-> 1/x over (say) the range from -5 to 5. Note the discontinuity at 0.

Good Hunting!

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