Definition of the approx. symbol












0












$begingroup$


Take an unending number, say e.g $π$. If we want to show $π$'s value, should we use the approximately notation or equal sign when writing:



$π = 3.14...$ or $π ≈ 3.14...$



This might be a really simple question, i don't know, but when i really started thinking about this i couldn't really decide. Technically we can't assign $π$ a "pure exact" value so does that restrict us to the approx. symbol? Or can we say actually say that $π = 3.14...$?



One thing for sure. $π ≈ 3.14$ is at least correct.



Thanks in advance!






notation definition approximation pi







share|cite|improve this question











$endgroup$












  • $begingroup$
    It’s not exactly equal, so the correct symbol to use is $approx$, not $ = $. You could use $ = $, but only when you use $pi$ rather than its decimal approximation.
    $endgroup$
    – KM101
    Dec 16 '18 at 12:26












  • $begingroup$
    It’s definitely not a bad question although I think most people wouldn’t be very picky about the symbol usage.
    $endgroup$
    – KM101
    Dec 16 '18 at 12:29










  • $begingroup$
    @KM101 yeah. Thank you anyways
    $endgroup$
    – Casimir Rönnlöf
    Dec 16 '18 at 12:30






  • 3




    $begingroup$
    But you have those three dots, "...", after that "3.14". That is the standard symbol representing the rest of the decimal representation of pi. In that case you should use "=". pi is approximately equal to 3.14 but exactly equal to 3.14....
    $endgroup$
    – user247327
    Dec 16 '18 at 12:36
















0












$begingroup$


Take an unending number, say e.g $π$. If we want to show $π$'s value, should we use the approximately notation or equal sign when writing:



$π = 3.14...$ or $π ≈ 3.14...$



This might be a really simple question, i don't know, but when i really started thinking about this i couldn't really decide. Technically we can't assign $π$ a "pure exact" value so does that restrict us to the approx. symbol? Or can we say actually say that $π = 3.14...$?



One thing for sure. $π ≈ 3.14$ is at least correct.



Thanks in advance!






notation definition approximation pi







share|cite|improve this question











$endgroup$












  • $begingroup$
    It’s not exactly equal, so the correct symbol to use is $approx$, not $ = $. You could use $ = $, but only when you use $pi$ rather than its decimal approximation.
    $endgroup$
    – KM101
    Dec 16 '18 at 12:26












  • $begingroup$
    It’s definitely not a bad question although I think most people wouldn’t be very picky about the symbol usage.
    $endgroup$
    – KM101
    Dec 16 '18 at 12:29










  • $begingroup$
    @KM101 yeah. Thank you anyways
    $endgroup$
    – Casimir Rönnlöf
    Dec 16 '18 at 12:30






  • 3




    $begingroup$
    But you have those three dots, "...", after that "3.14". That is the standard symbol representing the rest of the decimal representation of pi. In that case you should use "=". pi is approximately equal to 3.14 but exactly equal to 3.14....
    $endgroup$
    – user247327
    Dec 16 '18 at 12:36














0












0








0





$begingroup$


Take an unending number, say e.g $π$. If we want to show $π$'s value, should we use the approximately notation or equal sign when writing:



$π = 3.14...$ or $π ≈ 3.14...$



This might be a really simple question, i don't know, but when i really started thinking about this i couldn't really decide. Technically we can't assign $π$ a "pure exact" value so does that restrict us to the approx. symbol? Or can we say actually say that $π = 3.14...$?



One thing for sure. $π ≈ 3.14$ is at least correct.



Thanks in advance!






notation definition approximation pi







share|cite|improve this question











$endgroup$




Take an unending number, say e.g $π$. If we want to show $π$'s value, should we use the approximately notation or equal sign when writing:



$π = 3.14...$ or $π ≈ 3.14...$



This might be a really simple question, i don't know, but when i really started thinking about this i couldn't really decide. Technically we can't assign $π$ a "pure exact" value so does that restrict us to the approx. symbol? Or can we say actually say that $π = 3.14...$?



One thing for sure. $π ≈ 3.14$ is at least correct.



Thanks in advance!






notation definition approximation pi




notation definition approximation pi






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 16 '18 at 12:42









GNUSupporter 8964民主女神 地下教會

13.2k72547




13.2k72547










asked Dec 16 '18 at 12:25









Casimir RönnlöfCasimir Rönnlöf

1154




1154












  • $begingroup$
    It’s not exactly equal, so the correct symbol to use is $approx$, not $ = $. You could use $ = $, but only when you use $pi$ rather than its decimal approximation.
    $endgroup$
    – KM101
    Dec 16 '18 at 12:26












  • $begingroup$
    It’s definitely not a bad question although I think most people wouldn’t be very picky about the symbol usage.
    $endgroup$
    – KM101
    Dec 16 '18 at 12:29










  • $begingroup$
    @KM101 yeah. Thank you anyways
    $endgroup$
    – Casimir Rönnlöf
    Dec 16 '18 at 12:30






  • 3




    $begingroup$
    But you have those three dots, "...", after that "3.14". That is the standard symbol representing the rest of the decimal representation of pi. In that case you should use "=". pi is approximately equal to 3.14 but exactly equal to 3.14....
    $endgroup$
    – user247327
    Dec 16 '18 at 12:36


















  • $begingroup$
    It’s not exactly equal, so the correct symbol to use is $approx$, not $ = $. You could use $ = $, but only when you use $pi$ rather than its decimal approximation.
    $endgroup$
    – KM101
    Dec 16 '18 at 12:26












  • $begingroup$
    It’s definitely not a bad question although I think most people wouldn’t be very picky about the symbol usage.
    $endgroup$
    – KM101
    Dec 16 '18 at 12:29










  • $begingroup$
    @KM101 yeah. Thank you anyways
    $endgroup$
    – Casimir Rönnlöf
    Dec 16 '18 at 12:30






  • 3




    $begingroup$
    But you have those three dots, "...", after that "3.14". That is the standard symbol representing the rest of the decimal representation of pi. In that case you should use "=". pi is approximately equal to 3.14 but exactly equal to 3.14....
    $endgroup$
    – user247327
    Dec 16 '18 at 12:36
















$begingroup$
It’s not exactly equal, so the correct symbol to use is $approx$, not $ = $. You could use $ = $, but only when you use $pi$ rather than its decimal approximation.
$endgroup$
– KM101
Dec 16 '18 at 12:26






$begingroup$
It’s not exactly equal, so the correct symbol to use is $approx$, not $ = $. You could use $ = $, but only when you use $pi$ rather than its decimal approximation.
$endgroup$
– KM101
Dec 16 '18 at 12:26














$begingroup$
It’s definitely not a bad question although I think most people wouldn’t be very picky about the symbol usage.
$endgroup$
– KM101
Dec 16 '18 at 12:29




$begingroup$
It’s definitely not a bad question although I think most people wouldn’t be very picky about the symbol usage.
$endgroup$
– KM101
Dec 16 '18 at 12:29












$begingroup$
@KM101 yeah. Thank you anyways
$endgroup$
– Casimir Rönnlöf
Dec 16 '18 at 12:30




$begingroup$
@KM101 yeah. Thank you anyways
$endgroup$
– Casimir Rönnlöf
Dec 16 '18 at 12:30




3




3




$begingroup$
But you have those three dots, "...", after that "3.14". That is the standard symbol representing the rest of the decimal representation of pi. In that case you should use "=". pi is approximately equal to 3.14 but exactly equal to 3.14....
$endgroup$
– user247327
Dec 16 '18 at 12:36




$begingroup$
But you have those three dots, "...", after that "3.14". That is the standard symbol representing the rest of the decimal representation of pi. In that case you should use "=". pi is approximately equal to 3.14 but exactly equal to 3.14....
$endgroup$
– user247327
Dec 16 '18 at 12:36










2 Answers
2






active

oldest

votes


















4












$begingroup$

The statement
$$
tag{1} pi = 3.14ldots
$$
tells us the first three digits in the decimal expansion of $pi$, while acknowledging that there are more digits which we have not written explicitly. Statement (1) is valid and correct.






share|cite|improve this answer









$endgroup$





















    1












    $begingroup$

    I believe the implication with ellipsis is that "there's more to this number we're not posting here for whatever reason; just pretend it's all somehow here." Like we wouldn't say, as a simpler example,



    $$frac{1}{3} approx 0.33333...$$



    because it's pretty clear what goes in that "..." - an infinite amount of $3$'s. And, technically, since every number has an infinite decimal representation, with some numbers (I'll skip the details on which numbers those are) ending entirely $0$'s or $9$'s, we likewise wouldn't say



    $$1 approx 0.9999999999... ;;; text{or} ;;; 1 approx 1.000000000...$$



    It looks a little sillier when we do it with these simpler numbers, doesn't it? So in that sense, I think to say



    $$pi approx 3.14159...$$



    would be equally silly since we're basically saying with the ellipsis "the rest of the digits are here." We would be saying



    $$frac{1}{3} = 0.333... ;;;;;; 1 = 1.000... = 0.999... ;;;;;; pi = 3.14159...$$



    Granted, this is moreso a matter of how I've generally seen them used anecdotally and how I myself use them. I don't believe there's even a convention for this sort of thing since people are going to look at each representation essentially the same way - people aren't going to nitpick about "wait this text said "approximately" here."



    The key point with a good notation is ease of communication, I think we could agree on that much. I guess our notation isn't perfect since it lends itself to ambiguities like these, but the notation also lends itself to people not really caring either way in these sort of "fringe" cases since people get the point regardless.






    share|cite|improve this answer











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      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

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      active

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      active

      oldest

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      4












      $begingroup$

      The statement
      $$
      tag{1} pi = 3.14ldots
      $$
      tells us the first three digits in the decimal expansion of $pi$, while acknowledging that there are more digits which we have not written explicitly. Statement (1) is valid and correct.






      share|cite|improve this answer









      $endgroup$


















        4












        $begingroup$

        The statement
        $$
        tag{1} pi = 3.14ldots
        $$
        tells us the first three digits in the decimal expansion of $pi$, while acknowledging that there are more digits which we have not written explicitly. Statement (1) is valid and correct.






        share|cite|improve this answer









        $endgroup$
















          4












          4








          4





          $begingroup$

          The statement
          $$
          tag{1} pi = 3.14ldots
          $$
          tells us the first three digits in the decimal expansion of $pi$, while acknowledging that there are more digits which we have not written explicitly. Statement (1) is valid and correct.






          share|cite|improve this answer









          $endgroup$



          The statement
          $$
          tag{1} pi = 3.14ldots
          $$
          tells us the first three digits in the decimal expansion of $pi$, while acknowledging that there are more digits which we have not written explicitly. Statement (1) is valid and correct.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Dec 16 '18 at 12:39









          littleOlittleO

          29.8k646109




          29.8k646109























              1












              $begingroup$

              I believe the implication with ellipsis is that "there's more to this number we're not posting here for whatever reason; just pretend it's all somehow here." Like we wouldn't say, as a simpler example,



              $$frac{1}{3} approx 0.33333...$$



              because it's pretty clear what goes in that "..." - an infinite amount of $3$'s. And, technically, since every number has an infinite decimal representation, with some numbers (I'll skip the details on which numbers those are) ending entirely $0$'s or $9$'s, we likewise wouldn't say



              $$1 approx 0.9999999999... ;;; text{or} ;;; 1 approx 1.000000000...$$



              It looks a little sillier when we do it with these simpler numbers, doesn't it? So in that sense, I think to say



              $$pi approx 3.14159...$$



              would be equally silly since we're basically saying with the ellipsis "the rest of the digits are here." We would be saying



              $$frac{1}{3} = 0.333... ;;;;;; 1 = 1.000... = 0.999... ;;;;;; pi = 3.14159...$$



              Granted, this is moreso a matter of how I've generally seen them used anecdotally and how I myself use them. I don't believe there's even a convention for this sort of thing since people are going to look at each representation essentially the same way - people aren't going to nitpick about "wait this text said "approximately" here."



              The key point with a good notation is ease of communication, I think we could agree on that much. I guess our notation isn't perfect since it lends itself to ambiguities like these, but the notation also lends itself to people not really caring either way in these sort of "fringe" cases since people get the point regardless.






              share|cite|improve this answer











              $endgroup$


















                1












                $begingroup$

                I believe the implication with ellipsis is that "there's more to this number we're not posting here for whatever reason; just pretend it's all somehow here." Like we wouldn't say, as a simpler example,



                $$frac{1}{3} approx 0.33333...$$



                because it's pretty clear what goes in that "..." - an infinite amount of $3$'s. And, technically, since every number has an infinite decimal representation, with some numbers (I'll skip the details on which numbers those are) ending entirely $0$'s or $9$'s, we likewise wouldn't say



                $$1 approx 0.9999999999... ;;; text{or} ;;; 1 approx 1.000000000...$$



                It looks a little sillier when we do it with these simpler numbers, doesn't it? So in that sense, I think to say



                $$pi approx 3.14159...$$



                would be equally silly since we're basically saying with the ellipsis "the rest of the digits are here." We would be saying



                $$frac{1}{3} = 0.333... ;;;;;; 1 = 1.000... = 0.999... ;;;;;; pi = 3.14159...$$



                Granted, this is moreso a matter of how I've generally seen them used anecdotally and how I myself use them. I don't believe there's even a convention for this sort of thing since people are going to look at each representation essentially the same way - people aren't going to nitpick about "wait this text said "approximately" here."



                The key point with a good notation is ease of communication, I think we could agree on that much. I guess our notation isn't perfect since it lends itself to ambiguities like these, but the notation also lends itself to people not really caring either way in these sort of "fringe" cases since people get the point regardless.






                share|cite|improve this answer











                $endgroup$
















                  1












                  1








                  1





                  $begingroup$

                  I believe the implication with ellipsis is that "there's more to this number we're not posting here for whatever reason; just pretend it's all somehow here." Like we wouldn't say, as a simpler example,



                  $$frac{1}{3} approx 0.33333...$$



                  because it's pretty clear what goes in that "..." - an infinite amount of $3$'s. And, technically, since every number has an infinite decimal representation, with some numbers (I'll skip the details on which numbers those are) ending entirely $0$'s or $9$'s, we likewise wouldn't say



                  $$1 approx 0.9999999999... ;;; text{or} ;;; 1 approx 1.000000000...$$



                  It looks a little sillier when we do it with these simpler numbers, doesn't it? So in that sense, I think to say



                  $$pi approx 3.14159...$$



                  would be equally silly since we're basically saying with the ellipsis "the rest of the digits are here." We would be saying



                  $$frac{1}{3} = 0.333... ;;;;;; 1 = 1.000... = 0.999... ;;;;;; pi = 3.14159...$$



                  Granted, this is moreso a matter of how I've generally seen them used anecdotally and how I myself use them. I don't believe there's even a convention for this sort of thing since people are going to look at each representation essentially the same way - people aren't going to nitpick about "wait this text said "approximately" here."



                  The key point with a good notation is ease of communication, I think we could agree on that much. I guess our notation isn't perfect since it lends itself to ambiguities like these, but the notation also lends itself to people not really caring either way in these sort of "fringe" cases since people get the point regardless.






                  share|cite|improve this answer











                  $endgroup$



                  I believe the implication with ellipsis is that "there's more to this number we're not posting here for whatever reason; just pretend it's all somehow here." Like we wouldn't say, as a simpler example,



                  $$frac{1}{3} approx 0.33333...$$



                  because it's pretty clear what goes in that "..." - an infinite amount of $3$'s. And, technically, since every number has an infinite decimal representation, with some numbers (I'll skip the details on which numbers those are) ending entirely $0$'s or $9$'s, we likewise wouldn't say



                  $$1 approx 0.9999999999... ;;; text{or} ;;; 1 approx 1.000000000...$$



                  It looks a little sillier when we do it with these simpler numbers, doesn't it? So in that sense, I think to say



                  $$pi approx 3.14159...$$



                  would be equally silly since we're basically saying with the ellipsis "the rest of the digits are here." We would be saying



                  $$frac{1}{3} = 0.333... ;;;;;; 1 = 1.000... = 0.999... ;;;;;; pi = 3.14159...$$



                  Granted, this is moreso a matter of how I've generally seen them used anecdotally and how I myself use them. I don't believe there's even a convention for this sort of thing since people are going to look at each representation essentially the same way - people aren't going to nitpick about "wait this text said "approximately" here."



                  The key point with a good notation is ease of communication, I think we could agree on that much. I guess our notation isn't perfect since it lends itself to ambiguities like these, but the notation also lends itself to people not really caring either way in these sort of "fringe" cases since people get the point regardless.







                  share|cite|improve this answer














                  share|cite|improve this answer



                  share|cite|improve this answer








                  edited Dec 16 '18 at 12:40

























                  answered Dec 16 '18 at 12:35









                  Eevee TrainerEevee Trainer

                  6,0431936




                  6,0431936






























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