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
asked Nov 28 '18 at 12:26
Gurjinder
484414
|
show 1 more comment
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
asked Nov 28 '18 at 12:26
Gurjinder
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
|
show 1 more comment
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
asked Nov 28 '18 at 12:26
Gurjinder
484414
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
asked Nov 28 '18 at 12:26
Gurjinder
484414
asked Nov 28 '18 at 12:26
Gurjinder
484414
edited Nov 28 '18 at 12:28
asked Nov 28 '18 at 12:26
Gurjinder
484414
asked Nov 28 '18 at 12:26
Gurjinder
484414
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
|
show 1 more comment
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
|
show 1 more comment
1 Answer
1
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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 $i^2=-1$.
answered Nov 28 '18 at 12:32
SinTan1729
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
|
show 1 more comment
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1 Answer
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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 $i^2=-1$.
answered Nov 28 '18 at 12:32
SinTan1729
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
|
show 1 more comment
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 $i^2=-1$.
answered Nov 28 '18 at 12:32
SinTan1729
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
|
show 1 more comment
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 $i^2=-1$.
answered Nov 28 '18 at 12:32
SinTan1729
2,662723
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 $i^2=-1$.
answered Nov 28 '18 at 12:32
SinTan1729
2,662723
answered Nov 28 '18 at 12:32
SinTan1729
2,662723
answered Nov 28 '18 at 12:32
SinTan1729
2,662723
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
|
show 1 more comment
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
|
show 1 more comment
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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