A zero of a function is a value of the input for which the function value is 0. Properly speaking, we use this term only of functions, not of equations. That is, we talk about the zeros of f, not of f(x) = 0 (which would be redundant). Similarly, we shouldn't use the word "root" to mean a zero of a function; it applies only to equations.
A root of an equation means the same thing as solution, probably because it was thought of as the number from which the equation "grew", metaphorically. (It makes a little more sense to me in the case of square roots of numbers, from which squares grow. We even talk of "extracting the root" as if we were pulling up a radish -- which comes from the same "root" as "radical".)
I suspect that this usage is a lot older than the term solution, which has the same meaning when applied to an equation, but is more general. We tend to hold on to old words long after they could have been replaced.
See this page that I wrote a long time ago.
During my first year at university, I was taught that polynomials have roots, functions have zeros and equations have solutions. Since then, I've seen the words 'root', 'zero' and 'solution' interchanged to such an extent that the distinction hardly matters anymore (to me).
In other words, definitions in math can be flexible. Therefore, people who study math ought to be flexible, too. It took me a while to realize this because in my day mathematics was initially drilled into me as something factual, reliable and rigorous. That's fine, but not all "facts" are absolute, so be flexible. (If you research the words you asked about, you'll find each of them used both differently and synonymously.)
Here's another example.
Facts from high school: 0^0 has no definition, and zero is neither positive or negative.
Later, in college: 0^0 = 1, and zero may be defined as either positive, negative or neither.
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Were you really told that 0 can be defined as neg or pos?!! Wow!During my first year at university, I was taught that polynomials have roots, functions have zeros and equations have solutions. Since then, I've seen the words 'root', 'zero' and 'solution' interchanged to such an extent that the distinction hardly matters anymore (to me).
In other words, definitions in math can be flexible. Therefore, people who study math ought to be flexible, too. It took me a while to realize this because in my day mathematics was initially drilled into me as something factual, reliable and rigorous. That's fine, but not all "facts" are absolute, so be flexible. (If you research the words you asked about, you'll find each of them used both differently and synonymously.)
Here's another example.
Facts from high school: 0^0 has no definition, and zero is neither positive or negative.
Later, in college: 0^0 = 1, and zero may be defined as either positive, negative or neither.
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Sometimes roots are used in place of zeros. Authors may say "the roots of a polynomial function...". The definitions are not universal. Pay attention to your own materials and just remember they are generally interchangeable.
Were you really told that 0 can be defined as neg or pos?!! Wow!
I wasn't posting about me, in that second example, but I can see how it reads that way. I'll fix that, thank you.Were you really told that 0 can be defined as neg or pos? ...
I believe that "your own materials" means whatever you are learning from. I think you mentioned using a textbook; that is your "materials". Use the definitions in that book. (By the way, this is a reason I recommend working primarily from one textbook, rather than trying to get little bits from all over the web: They may confuse you by using different definitions or names for things, or a different order of presentation.)My own material? Am I a student at age 54?
After re-reading your post it is clear that it is an example. I still can't believe would say that 0 is positive or negative.I wasn't posting about me, in that second example, but I can see how it reads that way. I'll fix that, thank you.
Yes, you can find college textbooks where 0 has a sign (certain methods make use of that convention).
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Math people agree more that you think. There are some (silly) times where some definitions are different.
One book may start with a definition and then prove a theorem while another book will start off with theorem as their definition and then prove the definition. All mathematicians will be happy with this.
There are some theorems in real analysis that some mathematicians will not accept.
There are a set of mathematicians who do not believe that, for example, if the light swith is not on then must be is off. They will argue that there is a third option. These mathematicians (I think ) are called constructionist. They are a small breed and are not liked by (some) other mathematicians.
Yes, the situation is similar. Just as we need to speak with persons C,D,E and so on (until a consensus forms), so too we need experience with multiple viewpoints before our own perception gels (in general).I feel that professors are no different than representatives hired by different companies. Person A tells you [one thing, and person B tells you something else.]
I believe that "your own materials" means whatever you are learning from. I think you mentioned using a textbook; that is your "materials". Use the definitions in that book. (By the way, this is a reason I recommend working primarily from one textbook, rather than trying to get little bits from all over the web: They may confuse you by using different definitions or names for things, or a different order of presentation.)
And, yes, if you are studying something, even if it is on your own, then you are a student. That's all the word really means. (And, in fact, I have had students in community college who are your age.)
4. In NYC, there are students 50 and over. Unfortunately for me, I exhausted my PELL & TAP Financial Awards back in the 1990s to get my A.A. and B.A. degrees. I do not have money to return to college for a third diploma. With the MHF and other free math help sites and youtube, there is no need to return to the campus life.
Facts from high school: 0^0 has no definition, and zero is neither positive nor negative.
Later, in college: 0^0 = 1, and zero may be defined as either positive, negative or neither.
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Since you a NY resident you may qualify for the Excelsior Scholorship: https://www.hesc.ny.gov/pay-for-col...arships-awards/the-excelsior-scholarship.html
It has pretty hefty requirements though.
Your high-school teachers are "correct". Has "no definition" is misleading though because i don't doubt many sources define it that way. The debate will probably never be settled.