split - Help With Finding Real Roots - roots vs, Zeroes

[mmm4444bot]

The roots are the x-values where the function is 0

There's a terminology issue, here.

Function r is not defined by a polynomial. I think that the instructions should ask for the Real zeros, not the Real roots.

 

[DrSteve]

Re: Help With Finding Real Roots

This is the first I've heard that the word "root" should only be used for a polynomial. The expression "root of a function" does sound a bit unnatural to me when I think about it but I never realized (or thought about) that there was anything actually wrong with it. Wikipedia seems to think it's ok. Do you have a source that explicitly mentions that the word root should only be used for polynomials?

 

[mmm4444bot]

Wikipedia seems to think it's ok.

We can edit Wikipedia, to fix that, ya know. :wink:


Do you have a source

I do not have a written source to cite. The following "facts" were over time drilled into me by some PhD types at the University of Washington.

Polynomials have roots.

Functions have zeros.

Equations have solutions.

 

[mmm4444bot]

Ah, I thought my split request for this thread got lost, but here it is! (I wanted the split to go to odds-and-ends; although, this location is good enough.)

I told DrSteve that I would continue discussion about the terminology mentioned in this thread, after some research. I went to the math library at the University of Washington because I wanted to peruse math texts from the 1940s to see terminology with which those professors grew up.

My subsequent decision to throw out the window this entire issue over "roots vs zeros vs solutions" was not long in coming.

Authors back then not only referred to roots of functions but roots of many things, especially equations.

I found many examples where instructions read, "Find all Real roots of the equation" versus "Find all Real solutions of the equation", even in the complete absence of polynomials.

I also found references to statements like, "List roots of cosine, where theta is between -2Pi and 2Pi".

After considering many of the present-day changes taking hold in the way in which people communicate (face-to-face and in writing), perhaps fine details are no longer important as long as parties achieve mutual comprehension.

In short, if a student understands that they're looking for a value that causes some object to evaluate to zero, I'll cheer that understanding and care not what descriptive names are used.

PS: I wish that I could remember more about the wording in presentations and exercises in my courses, where the distinction of root vs zero vs solution actually provided important context. It seems like the distinction was once important.

 

[Deleted member 4993]

One good reference could be:

http://mathworld.wolfram.com/Root.html