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Sep 15, 2018 at 21:11 comment added Roman Odaisky @Number Makes sense. Then maybe a more accurate distinction would be that cancellation is removal of a factor together with its multiplicative inverse, which may or may not lead to elimination where one or more variables no longer participate in the expression.
Sep 15, 2018 at 17:57 comment added Bill Dubuque @Roman But cancellation generally is not the same as variable elimination, e,g. see the counterexample I gave in the comment preceding yours.
Sep 15, 2018 at 16:11 comment added Roman Odaisky I would say “eliminate” when it’s deliberate (“To solve this, we need to eliminate one of the variables. Let’s start with $y$.”) and “cancel” without such emphasis (“Observe that the same expression appears both in the numerator and the denominator, so it cancels out.”)
Sep 14, 2018 at 22:34 comment added Bill Dubuque @guest e.g. we can cancel $a$ from $\dfrac{ac+a^2}a$ to get $c+a$ but "eliminate $a$" is not what we did.
Sep 14, 2018 at 21:17 comment added Bill Dubuque @jpmc26 Please read more carefully.The discussion concerns whether "eliminate $a$" is standard usage to describe the cancellation laws $\, ax = ac\,\Rightarrow\,x = c\ $ or $\ x = \dfrac{ac}a\,\Rightarrow\, x = c\quad$
Sep 14, 2018 at 21:12 comment added Bill Dubuque @guest Nothing I wrote here is based on "hunches". If anyone can supply examples that contradict my claims about usage then I would be most interested to see them.
Sep 14, 2018 at 21:04 comment added jpmc26 @Number Classrooms and people standing at a black/whiteboard discussing math are not "reputable publications." Are you saying you've never heard anyone say "cancelled"? Or just that you've never seen it in peer reviewed work or something? And what about casual sources that are not "reputable"?
Sep 14, 2018 at 20:34 comment added guest Number: It's good to have a good ear and to listen to your hunches but I would not be so quick to assume that your hunches are correct. At this point, you are just saying "sounds strange to me" and putting burden of proof on others to disprove you.
Sep 14, 2018 at 19:59 comment added Bill Dubuque @jpmc26 Yes, I'm American and I've been teaching algebra at all levels for almost 4 decades (e.g. I am one of the most active algebra and number theory teachers on Math.SE, and ditto for earlier sites like sci.math, Ask an Algebraist, etc). So I have broad exposure to English algebraic language.I don't recall ever seeing "eliminate" used instead of "cancel" in a reputable publication by an author whose first language is English.
Sep 14, 2018 at 19:49 comment added jpmc26 @Number Are you a native English speaker, and what country's dialect do you speak? I can assure you that I've never encountered an American in a STEM field who would bat an eye at using "cancelled" to describe eliminating multiplicative constants (even fractional ones) from equations. If anything, using "eliminate" is much less common.
Sep 14, 2018 at 18:44 comment added Bill Dubuque @Gerald But your link refers to (Gaussian) elimination of variables in systems of (linear) equations, not to cancelling a factor in a single equation. I've never seen elimination used instead of cancellation in the single equation case as in the OP.
Sep 14, 2018 at 18:14 comment added Gerald Edgar See for example en.wikipedia.org/wiki/… It is true that "cancel" and "eliminate" sometimes have different meanings, but they both qualify as "variables disappear when solving".
Sep 14, 2018 at 18:11 comment added guest I am used to either cancel or eliminate and it does not sound odd to my ear and I am a native English speaker. ceemrr.com/Geometry2/Eliminating_Fractions/…
Sep 14, 2018 at 17:30 comment added Moshe Katz @Number I have heard it, but only from professors who are not native English speakers and are translating from their native languages. (That's not to say that it's incorrect, I just found it to be less common.)
Sep 14, 2018 at 15:45 comment added Bill Dubuque I've never heard "eliminated" used as a synonym for "cancelled". Do you have any links exhibiting such?
Sep 14, 2018 at 12:45 review Low quality posts
Sep 14, 2018 at 13:25
Sep 14, 2018 at 12:29 history answered Gerald Edgar CC BY-SA 4.0