Is it appropriate to consider a hole in the graph a zero?Can the graph of $x^x$ have a real-valued plot below...

Averaging over columns while ignoring zero entries

Precision notation for voltmeters

Why does a car's steering wheel get lighter with increasing speed

Why isn't P and P/poly trivially the same?

Vector-transposing function

Tabular environment - text vertically positions itself by bottom of tikz picture in adjacent cell

I am the person who abides by rules but breaks the rules . Who am I

An Undercover Army

Why do we say 'Pairwise Disjoint', rather than 'Disjoint'?

Unidentified signals on FT8 frequencies

Is there a logarithm base for which the logarithm becomes an identity function?

What does "rhumatis" mean?

What does it take to become a wilderness skills guide as a business?

Mixed Feelings - What am I

Why is there an extra space when I type "ls" on the Desktop?

Boss Telling direct supervisor I snitched

Why aren't there more Gauls like Obelix?

Use Mercury as quenching liquid for swords?

Is "cogitate" used appropriately in "I cogitate that success relies on hard work"?

Can I challenge the interviewer to give me a proper technical feedback?

Who has more? Ireland or Iceland?

How to educate team mate to take screenshots for bugs with out unwanted stuff

How to recover against Snake as a heavyweight character?

Rationale to prefer local variables over instance variables?



Is it appropriate to consider a hole in the graph a zero?


Can the graph of $x^x$ have a real-valued plot below zero?How to evaluate a zero of the Riemann zeta function?Graph the function and apply the appropriate transformations $y = (1)/( x + 4)$Converting a graph into a functionWhy don't graphing tools represent holes in a graph?Calculating equation for a graphGraph of a Function or a Just a Relation?Take the function $f(x)=8x+120$. Find a function $g(x)$ which contains the point $(0,0)$ and is asymptotic to $f(x)$.Consider the family of equations $y=x^n$ with the integer parameter n.When is it appropriate to neglect the arguments of the function?













1












$begingroup$


Let there be a function $$f(x) = frac{x^2}{e^x-1}$$ which has a hole at $x=0$.
It also approaches $f(x) = 0$ at this point. Would it be appropriate to call this hole a "zero" or not?






functions terminology roots graphing-functions







share|cite|improve this question









$endgroup$

















    1












    $begingroup$


    Let there be a function $$f(x) = frac{x^2}{e^x-1}$$ which has a hole at $x=0$.
    It also approaches $f(x) = 0$ at this point. Would it be appropriate to call this hole a "zero" or not?






    functions terminology roots graphing-functions







    share|cite|improve this question









    $endgroup$















      1












      1








      1





      $begingroup$


      Let there be a function $$f(x) = frac{x^2}{e^x-1}$$ which has a hole at $x=0$.
      It also approaches $f(x) = 0$ at this point. Would it be appropriate to call this hole a "zero" or not?






      functions terminology roots graphing-functions







      share|cite|improve this question









      $endgroup$




      Let there be a function $$f(x) = frac{x^2}{e^x-1}$$ which has a hole at $x=0$.
      It also approaches $f(x) = 0$ at this point. Would it be appropriate to call this hole a "zero" or not?






      functions terminology roots graphing-functions




      functions terminology roots graphing-functions






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked yesterday









      AnadactotheAnadactothe

      13211




      13211






















          1 Answer
          1






          active

          oldest

          votes


















          1












          $begingroup$

          A zero is a point $a$ where $f(a) = 0$. In your case, $f(0)$ is undefined, so no, $x=0$ is not a zero.



          On the other hand, since the discontinuity is removable, we can plug the hole by defining
          $$g(x)=begin{cases}
          f(x), &x neq 0\
          0, &x=0
          end{cases}$$
          in which case $x=0$ is indeed a zero of $g(x)$.






          share|cite|improve this answer









          $endgroup$













            Your Answer





            StackExchange.ifUsing("editor", function () {
            return StackExchange.using("mathjaxEditing", function () {
            StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
            StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
            });
            });
            }, "mathjax-editing");

            StackExchange.ready(function() {
            var channelOptions = {
            tags: "".split(" "),
            id: "69"
            };
            initTagRenderer("".split(" "), "".split(" "), channelOptions);

            StackExchange.using("externalEditor", function() {
            // Have to fire editor after snippets, if snippets enabled
            if (StackExchange.settings.snippets.snippetsEnabled) {
            StackExchange.using("snippets", function() {
            createEditor();
            });
            }
            else {
            createEditor();
            }
            });

            function createEditor() {
            StackExchange.prepareEditor({
            heartbeatType: 'answer',
            autoActivateHeartbeat: false,
            convertImagesToLinks: true,
            noModals: true,
            showLowRepImageUploadWarning: true,
            reputationToPostImages: 10,
            bindNavPrevention: true,
            postfix: "",
            imageUploader: {
            brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
            contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
            allowUrls: true
            },
            noCode: true, onDemand: true,
            discardSelector: ".discard-answer"
            ,immediatelyShowMarkdownHelp:true
            });


            }
            });














            draft saved

            draft discarded


















            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3139291%2fis-it-appropriate-to-consider-a-hole-in-the-graph-a-zero%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown

























            1 Answer
            1






            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            1












            $begingroup$

            A zero is a point $a$ where $f(a) = 0$. In your case, $f(0)$ is undefined, so no, $x=0$ is not a zero.



            On the other hand, since the discontinuity is removable, we can plug the hole by defining
            $$g(x)=begin{cases}
            f(x), &x neq 0\
            0, &x=0
            end{cases}$$
            in which case $x=0$ is indeed a zero of $g(x)$.






            share|cite|improve this answer









            $endgroup$


















              1












              $begingroup$

              A zero is a point $a$ where $f(a) = 0$. In your case, $f(0)$ is undefined, so no, $x=0$ is not a zero.



              On the other hand, since the discontinuity is removable, we can plug the hole by defining
              $$g(x)=begin{cases}
              f(x), &x neq 0\
              0, &x=0
              end{cases}$$
              in which case $x=0$ is indeed a zero of $g(x)$.






              share|cite|improve this answer









              $endgroup$
















                1












                1








                1





                $begingroup$

                A zero is a point $a$ where $f(a) = 0$. In your case, $f(0)$ is undefined, so no, $x=0$ is not a zero.



                On the other hand, since the discontinuity is removable, we can plug the hole by defining
                $$g(x)=begin{cases}
                f(x), &x neq 0\
                0, &x=0
                end{cases}$$
                in which case $x=0$ is indeed a zero of $g(x)$.






                share|cite|improve this answer









                $endgroup$



                A zero is a point $a$ where $f(a) = 0$. In your case, $f(0)$ is undefined, so no, $x=0$ is not a zero.



                On the other hand, since the discontinuity is removable, we can plug the hole by defining
                $$g(x)=begin{cases}
                f(x), &x neq 0\
                0, &x=0
                end{cases}$$
                in which case $x=0$ is indeed a zero of $g(x)$.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered yesterday









                ThéophileThéophile

                20.2k13047




                20.2k13047






























                    draft saved

                    draft discarded




















































                    Thanks for contributing an answer to Mathematics Stack Exchange!


                    • Please be sure to answer the question. Provide details and share your research!

                    But avoid …



                    • Asking for help, clarification, or responding to other answers.

                    • Making statements based on opinion; back them up with references or personal experience.


                    Use MathJax to format equations. MathJax reference.


                    To learn more, see our tips on writing great answers.




                    draft saved


                    draft discarded














                    StackExchange.ready(
                    function () {
                    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3139291%2fis-it-appropriate-to-consider-a-hole-in-the-graph-a-zero%23new-answer', 'question_page');
                    }
                    );

                    Post as a guest















                    Required, but never shown





















































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown

































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown







                    -

                    Popular posts from this blog

                    Nidaros erkebispedøme

                    Image
                    For det lutherske bispedømet, sjå Nidaros bispedøme. Nidaros erkebispedøme var eit katolsk erkebispedøme med sete i Nidaros. Det vart oppretta av kong Olav Kyrre mellom 1070 og 1080 som bispedøme. Bispedømet vart opphøgd til erkebispedøme i 1153. Erkebispedømet vart innstifta av pave Anastasius IV i 1154, og var i funksjon fram til reformasjonen i 1537. Erkebiskopen sitt hovudsete var Erkebispegarden, rett ved domkyrkja Nidarosdomen. Frå 1152 til 1154 var Nicholas Breakspear i Skandinavia som paveleg utsending, og organiserte opprettinga av erkesetet. Innhaldsliste 1 Utbreiing og jurisdiksjon 2 Overhyrdar 2.1 Lydbiskopar 3 Biskopar 3.1 Biskopar 3.2 Erkebiskopar Utbreiing og jurisdiksjon | Kart over den nordiske kyrkjeprovinsen (1153-1387) Erkebispedømet omfatta i tillegg til Noreg øyane i vest i Noregsveldet. Nidaros var eit metropolitanerkebispedøme med fylgjande underliggjande bispedøme suffraganar: Bj...
                    Read more

                    Birsay

                    Image
                    Tettstaden Birsay på Orknøyane. Ruinane av jarleplasset om lag midt i biletet. (Fotografi frå 2012) Utsikt mot Birsay og Brough of Brisay (fotografi frå 2009) Birsay er ein tettstad i eit sokn (parish) med same namn, nordvest på øya Mainland [Note 1] på Orknøyane, om lag 31 km frå Kirkwall. Staden er omtala fleire stader i Orknøyingasoga [1] , der han er kalla «Byrgesherad» (norrønt: Birgisherað ). Namnet skriv seg truleg frå elvenamnet Birgisá [2] . Innhaldsliste 1 Den gamle hovudstaden 2 Bispesetet 3 Jarlepalasset 4 Kjelder og utfyllande opplysningar 4.1 Notar 4.2 Fotnotar 4.3 Bakgrunnsstoff Den gamle hovudstaden | Hovudartikkelen for dette emnet er Torfinn Sigurdsson . Soknet er i dag i hovudsak ei jordbrukskommune men er mest kjend for dei mange kulturminna i området. Tettstaden Birsay blir gjerne omtala som «den gamle hovudstaden på Orknøyane» [3] , og ein viser d...
                    Read more

                    Was Woodrow Wilson really a Liberal?Was World War I a war of liberals against authoritarians?Founding Fathers...

                    Image
                    Do VLANs within a subnet need to have their own subnet for router on a stick? What are the differences between the usage of 'it' and 'they'? Dragon forelimb placement How do we improve the relationship with a client software team that performs poorly and is becoming less collaborative? What typically incentivizes a professor to change jobs to a lower ranking university? How to write a macro that is braces sensitive? Modeling an IPv4 Address Writing rule stating superpower from different root cause is bad writing Can I ask the recruiters in my resume to put the reason why I am rejected? Approximately how much travel t...
                    Read more