Suppose I draw an arbitrary curve on a leaf, and then I put an orthonormal coordinate system on that leaf. Is there a function rule for this, without exception, or can you not determine a rule for every curve (of course I draw a “function”, ie each point of the domain has exactly one image (so it is also continuous)!
Answer
Dear Bart,
It depends on what you call a “function rule”. The following job instruction describes your job:
f: x->f(x): f(x) is the value of the ordinate corresponding to the abscissa x, as drawn on the paper
Now that’s not what you mean, I guess. Your question is actually: can any function rule be expressed in terms of elementary functions such as x^2, sin(x), tg(x), log(x), etc.
Then the answer is no.
Greetings,
Philippe
Answered by
Prof. dr. Dr Philippe Tassin
applied physics; optics; photonics; physics
Avenue de la Plein 2 1050 Ixelles
http://www.vub.ac.be/
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