Should you write $i = sqrt{-1}$ or $i := sqrt{-1}$?












0














Is one of the following more correct than the other, or does it simply not matter?



$i = sqrt{-1} quad$ or $quad i := sqrt{-1}$?



Here I am using $:=$ to mean "defined to be equal to."






complex-analysis complex-numbers notation







share|cite|improve this question




















  • 6




    I wouldn’t write either.
    – Randall
    Nov 28 '18 at 12:28










  • @Randall okay, what could you write instead?
    – Gurjinder
    Nov 28 '18 at 12:32






  • 1




    @Randall Do you mind expanding on this comment? Otherwise is not very useful for the OP
    – caverac
    Nov 28 '18 at 12:32






  • 2




    $i^2=-1$........
    – Randall
    Nov 28 '18 at 12:32










  • @caverac You are correct. Fair point.
    – Randall
    Nov 28 '18 at 12:33
















0














Is one of the following more correct than the other, or does it simply not matter?



$i = sqrt{-1} quad$ or $quad i := sqrt{-1}$?



Here I am using $:=$ to mean "defined to be equal to."






complex-analysis complex-numbers notation







share|cite|improve this question




















  • 6




    I wouldn’t write either.
    – Randall
    Nov 28 '18 at 12:28










  • @Randall okay, what could you write instead?
    – Gurjinder
    Nov 28 '18 at 12:32






  • 1




    @Randall Do you mind expanding on this comment? Otherwise is not very useful for the OP
    – caverac
    Nov 28 '18 at 12:32






  • 2




    $i^2=-1$........
    – Randall
    Nov 28 '18 at 12:32










  • @caverac You are correct. Fair point.
    – Randall
    Nov 28 '18 at 12:33














0












0








0







Is one of the following more correct than the other, or does it simply not matter?



$i = sqrt{-1} quad$ or $quad i := sqrt{-1}$?



Here I am using $:=$ to mean "defined to be equal to."






complex-analysis complex-numbers notation







share|cite|improve this question















Is one of the following more correct than the other, or does it simply not matter?



$i = sqrt{-1} quad$ or $quad i := sqrt{-1}$?



Here I am using $:=$ to mean "defined to be equal to."






complex-analysis complex-numbers notation




complex-analysis complex-numbers notation






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 28 '18 at 12:28

























asked Nov 28 '18 at 12:26









Gurjinder

484414




484414








  • 6




    I wouldn’t write either.
    – Randall
    Nov 28 '18 at 12:28










  • @Randall okay, what could you write instead?
    – Gurjinder
    Nov 28 '18 at 12:32






  • 1




    @Randall Do you mind expanding on this comment? Otherwise is not very useful for the OP
    – caverac
    Nov 28 '18 at 12:32






  • 2




    $i^2=-1$........
    – Randall
    Nov 28 '18 at 12:32










  • @caverac You are correct. Fair point.
    – Randall
    Nov 28 '18 at 12:33














  • 6




    I wouldn’t write either.
    – Randall
    Nov 28 '18 at 12:28










  • @Randall okay, what could you write instead?
    – Gurjinder
    Nov 28 '18 at 12:32






  • 1




    @Randall Do you mind expanding on this comment? Otherwise is not very useful for the OP
    – caverac
    Nov 28 '18 at 12:32






  • 2




    $i^2=-1$........
    – Randall
    Nov 28 '18 at 12:32










  • @caverac You are correct. Fair point.
    – Randall
    Nov 28 '18 at 12:33








6




6




I wouldn’t write either.
– Randall
Nov 28 '18 at 12:28




I wouldn’t write either.
– Randall
Nov 28 '18 at 12:28












@Randall okay, what could you write instead?
– Gurjinder
Nov 28 '18 at 12:32




@Randall okay, what could you write instead?
– Gurjinder
Nov 28 '18 at 12:32




1




1




@Randall Do you mind expanding on this comment? Otherwise is not very useful for the OP
– caverac
Nov 28 '18 at 12:32




@Randall Do you mind expanding on this comment? Otherwise is not very useful for the OP
– caverac
Nov 28 '18 at 12:32




2




2




$i^2=-1$........
– Randall
Nov 28 '18 at 12:32




$i^2=-1$........
– Randall
Nov 28 '18 at 12:32












@caverac You are correct. Fair point.
– Randall
Nov 28 '18 at 12:33




@caverac You are correct. Fair point.
– Randall
Nov 28 '18 at 12:33










1 Answer
1






active

oldest

votes


















6














None of them are correct as the square root is not a single-valued function. The best expression (i.e. simplest) defining $i$ would be $i^2=-1$.






share|cite|improve this answer





















  • Okay fair enough. Why not $i^2 := -1$?
    – Gurjinder
    Nov 28 '18 at 12:37










  • Okay, I think the OP had an error. Let's think about $i$ as $pmsqrt{-1}$. $i=pmsqrt{-1}$ or $i:=pmsqrt{-1}$?
    – manooooh
    Nov 28 '18 at 12:39










  • You can write that. $:=$ is usually used in definitions. Since $i$ is widely used, we don't need to "define" it everytime. Also, that notation is hardly ever used. But if you want, no one is stopping you (possibly once in a discussion/problem).
    – SinTan1729
    Nov 28 '18 at 12:39












  • @manooooh Okay, thank you for the clarification.
    – Gurjinder
    Nov 28 '18 at 12:44












  • @SinTan1729 Okay, thank you for the clarification.
    – Gurjinder
    Nov 28 '18 at 12:45











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1 Answer
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active

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1 Answer
1






active

oldest

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active

oldest

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active

oldest

votes









6














None of them are correct as the square root is not a single-valued function. The best expression (i.e. simplest) defining $i$ would be $i^2=-1$.






share|cite|improve this answer





















  • Okay fair enough. Why not $i^2 := -1$?
    – Gurjinder
    Nov 28 '18 at 12:37










  • Okay, I think the OP had an error. Let's think about $i$ as $pmsqrt{-1}$. $i=pmsqrt{-1}$ or $i:=pmsqrt{-1}$?
    – manooooh
    Nov 28 '18 at 12:39










  • You can write that. $:=$ is usually used in definitions. Since $i$ is widely used, we don't need to "define" it everytime. Also, that notation is hardly ever used. But if you want, no one is stopping you (possibly once in a discussion/problem).
    – SinTan1729
    Nov 28 '18 at 12:39












  • @manooooh Okay, thank you for the clarification.
    – Gurjinder
    Nov 28 '18 at 12:44












  • @SinTan1729 Okay, thank you for the clarification.
    – Gurjinder
    Nov 28 '18 at 12:45
















6














None of them are correct as the square root is not a single-valued function. The best expression (i.e. simplest) defining $i$ would be $i^2=-1$.






share|cite|improve this answer





















  • Okay fair enough. Why not $i^2 := -1$?
    – Gurjinder
    Nov 28 '18 at 12:37










  • Okay, I think the OP had an error. Let's think about $i$ as $pmsqrt{-1}$. $i=pmsqrt{-1}$ or $i:=pmsqrt{-1}$?
    – manooooh
    Nov 28 '18 at 12:39










  • You can write that. $:=$ is usually used in definitions. Since $i$ is widely used, we don't need to "define" it everytime. Also, that notation is hardly ever used. But if you want, no one is stopping you (possibly once in a discussion/problem).
    – SinTan1729
    Nov 28 '18 at 12:39












  • @manooooh Okay, thank you for the clarification.
    – Gurjinder
    Nov 28 '18 at 12:44












  • @SinTan1729 Okay, thank you for the clarification.
    – Gurjinder
    Nov 28 '18 at 12:45














6












6








6






None of them are correct as the square root is not a single-valued function. The best expression (i.e. simplest) defining $i$ would be $i^2=-1$.






share|cite|improve this answer












None of them are correct as the square root is not a single-valued function. The best expression (i.e. simplest) defining $i$ would be $i^2=-1$.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Nov 28 '18 at 12:32









SinTan1729

2,662723




2,662723












  • Okay fair enough. Why not $i^2 := -1$?
    – Gurjinder
    Nov 28 '18 at 12:37










  • Okay, I think the OP had an error. Let's think about $i$ as $pmsqrt{-1}$. $i=pmsqrt{-1}$ or $i:=pmsqrt{-1}$?
    – manooooh
    Nov 28 '18 at 12:39










  • You can write that. $:=$ is usually used in definitions. Since $i$ is widely used, we don't need to "define" it everytime. Also, that notation is hardly ever used. But if you want, no one is stopping you (possibly once in a discussion/problem).
    – SinTan1729
    Nov 28 '18 at 12:39












  • @manooooh Okay, thank you for the clarification.
    – Gurjinder
    Nov 28 '18 at 12:44












  • @SinTan1729 Okay, thank you for the clarification.
    – Gurjinder
    Nov 28 '18 at 12:45


















  • Okay fair enough. Why not $i^2 := -1$?
    – Gurjinder
    Nov 28 '18 at 12:37










  • Okay, I think the OP had an error. Let's think about $i$ as $pmsqrt{-1}$. $i=pmsqrt{-1}$ or $i:=pmsqrt{-1}$?
    – manooooh
    Nov 28 '18 at 12:39










  • You can write that. $:=$ is usually used in definitions. Since $i$ is widely used, we don't need to "define" it everytime. Also, that notation is hardly ever used. But if you want, no one is stopping you (possibly once in a discussion/problem).
    – SinTan1729
    Nov 28 '18 at 12:39












  • @manooooh Okay, thank you for the clarification.
    – Gurjinder
    Nov 28 '18 at 12:44












  • @SinTan1729 Okay, thank you for the clarification.
    – Gurjinder
    Nov 28 '18 at 12:45
















Okay fair enough. Why not $i^2 := -1$?
– Gurjinder
Nov 28 '18 at 12:37




Okay fair enough. Why not $i^2 := -1$?
– Gurjinder
Nov 28 '18 at 12:37












Okay, I think the OP had an error. Let's think about $i$ as $pmsqrt{-1}$. $i=pmsqrt{-1}$ or $i:=pmsqrt{-1}$?
– manooooh
Nov 28 '18 at 12:39




Okay, I think the OP had an error. Let's think about $i$ as $pmsqrt{-1}$. $i=pmsqrt{-1}$ or $i:=pmsqrt{-1}$?
– manooooh
Nov 28 '18 at 12:39












You can write that. $:=$ is usually used in definitions. Since $i$ is widely used, we don't need to "define" it everytime. Also, that notation is hardly ever used. But if you want, no one is stopping you (possibly once in a discussion/problem).
– SinTan1729
Nov 28 '18 at 12:39






You can write that. $:=$ is usually used in definitions. Since $i$ is widely used, we don't need to "define" it everytime. Also, that notation is hardly ever used. But if you want, no one is stopping you (possibly once in a discussion/problem).
– SinTan1729
Nov 28 '18 at 12:39














@manooooh Okay, thank you for the clarification.
– Gurjinder
Nov 28 '18 at 12:44






@manooooh Okay, thank you for the clarification.
– Gurjinder
Nov 28 '18 at 12:44














@SinTan1729 Okay, thank you for the clarification.
– Gurjinder
Nov 28 '18 at 12:45




@SinTan1729 Okay, thank you for the clarification.
– Gurjinder
Nov 28 '18 at 12:45


















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