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This is the proof

http://planetmath.org/encyclopedia/ProofOfPropertiesOfTheExponential.html [Broken]

I wonder what they do when they describe monotnicity for integers. Why is

[tex]x^p<y<p[/tex] when x<y and p is a positive integer? What if p was really large?

and further down in the part homogeneity for rational exponents is there a typo there? Should not

[tex] (v_1 v_2)^n > (xy)^m[/tex]

and not

[tex] (v_1 v_2)^n < (xy)^m[/tex]

or?

http://planetmath.org/encyclopedia/ProofOfPropertiesOfTheExponential.html [Broken]

I wonder what they do when they describe monotnicity for integers. Why is

[tex]x^p<y<p[/tex] when x<y and p is a positive integer? What if p was really large?

and further down in the part homogeneity for rational exponents is there a typo there? Should not

[tex] (v_1 v_2)^n > (xy)^m[/tex]

and not

[tex] (v_1 v_2)^n < (xy)^m[/tex]

or?

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