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11. Suppose F is an infinite field and f.ge Frj. Show that if f # g t.pdf

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11. Suppose F is an infinite field and f.ge Frj. Show that if f # g then the functions they induce (from F to F) are different Solution If the two components (vectors in a field) are not equal, then the induced functions F(x) at x=f can not be equal to F(x) at x=g as the function is dependent on single variable. So the function that has one to one mapping can not be equal at two different points..

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11. Suppose F is an infinite field and f.ge Frj. Show that if f # g then the functions they induce (from F to F) are different Solution If the two components (vectors in a field) are not equal, then the induced functions F(x) at x=f can not be equal to F(x) at x=g as the function is dependent on single variable. So the function that has one to one mapping can not be equal at two different points.

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