- #1
3trQN
- 337
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Hi peeps! I have some minor calculus problem, well confusion is the problem.
I was playing about with some numbers while doing some differential calc problems, when i started to explore a little further one expression.
[tex]
y=f(x)=\sqrt[m]{\frac{1}{x^{n}}}=x^{-\frac{n}{m}}
[/tex] ----- (1)
Of course i thought about rational numbers and primes, and that a rational number is any number which can be expressed as the quotient of two integers.
So assuming:
[tex]n \in Z^+[/tex]
[tex]m \in Z^+[/tex]
I then thought about what if the exponent was a prime, so
[tex]\frac{p}{m}[/tex] where [tex]p=prime[/tex]
Then for:
[tex]1 < m < p[/tex]
The exponent would allways be irrational.
Upon seeing the inequality expresison i wrote down i wondered if there was a link between it and the triangle inequality expression. Is this the case?
I was playing about with some numbers while doing some differential calc problems, when i started to explore a little further one expression.
[tex]
y=f(x)=\sqrt[m]{\frac{1}{x^{n}}}=x^{-\frac{n}{m}}
[/tex] ----- (1)
Of course i thought about rational numbers and primes, and that a rational number is any number which can be expressed as the quotient of two integers.
So assuming:
[tex]n \in Z^+[/tex]
[tex]m \in Z^+[/tex]
I then thought about what if the exponent was a prime, so
[tex]\frac{p}{m}[/tex] where [tex]p=prime[/tex]
Then for:
[tex]1 < m < p[/tex]
The exponent would allways be irrational.
Upon seeing the inequality expresison i wrote down i wondered if there was a link between it and the triangle inequality expression. Is this the case?
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