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The word degree comes from Latin degradus (through French), which means something like step down.

The word order comes from Latin ordinem (through French too), which means row,rank.

Is there a reason why orders are called orders in maths and degrees, degrees? For example, is there fundamental reasons why the number of derivatives in an ODE is called order and not degree, and the degree of a polynomial degree and not order?

anderstood
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    This terminology is pretty mixed up in mathematics, its usage is perhaps less consistent than you might imagine. For instance, the number $n$ is called the degree of the polynomial $P(z)=(z-a)^n$ and it is also called the order of the zero $z=a$ of $P(z)$. – Lee Mosher May 08 '15 at 00:35
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    @LeeMosher That's precisely because I can't see fundamental reason to this terminology that I am asking if there is any :-) The answer might very well be no! – anderstood May 08 '15 at 00:36
  • Etymology often has very little to do with meaning, especially in mathematics. You may find it helpful to look up "order" at http://jeff560.tripod.com/o.html, – Robert Israel May 08 '15 at 00:38
  • @RobertIsrael Very interesting, thank you. This tend to confirm there is no reason other than historical ones. – anderstood May 08 '15 at 00:42
  • Analytic functions have zeros with orders, polynomials have roots with multiplicities. The meaning is essentially the same (at least if you're working in the field $\mathbb C$). – Robert Israel May 08 '15 at 00:44

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