Why is there both `:=` and `=` used in set notation? [duplicate]

Clash Royale CLAN TAG#URR8PPP

up vote
7
down vote

favorite

2

This question already has an answer here:

• 
  Difference between $:=$ and $=$
  
  3 answers
  
  

I see two kinds of equal signs in different resources in regards to defining sets. One is := and the other is =

An example : S = 1, 2, 3 or S := 1, 2, 3

I realized that resources concerned with mathematical analysis uses the latter whereas others use the former.

Is there any difference in the meaning of both notations?

elementary-set-theory notation

share|cite|improve this question

edited Aug 27 at 11:06

Brahadeesh

4,12331550

asked Aug 27 at 10:51

nmd_07

506

marked as duplicate by Carsten S, BlueRaja - Danny Pflughoeft, quid♦ Aug 27 at 17:15

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  The := symbol is usually 'defined as', rather than 'equal to'.
  – Bill Wallis
  Aug 27 at 10:52
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  It seems to me that := is introduced sometime later.
  – nmd_07
  Aug 27 at 10:53
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  In some programming languages like Go := used to define and assign, whereas = is for just assignment. Maybe this analogy help you
  – Grijesh Chauhan
  Aug 27 at 16:32
  

  
  
  
  

add a comment | 

up vote
7
down vote

favorite

2

This question already has an answer here:

• 
  Difference between $:=$ and $=$
  
  3 answers
  
  

I see two kinds of equal signs in different resources in regards to defining sets. One is := and the other is =

An example : S = 1, 2, 3 or S := 1, 2, 3

I realized that resources concerned with mathematical analysis uses the latter whereas others use the former.

Is there any difference in the meaning of both notations?

elementary-set-theory notation

share|cite|improve this question

edited Aug 27 at 11:06

Brahadeesh

4,12331550

asked Aug 27 at 10:51

nmd_07

506

marked as duplicate by Carsten S, BlueRaja - Danny Pflughoeft, quid♦ Aug 27 at 17:15

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  The := symbol is usually 'defined as', rather than 'equal to'.
  – Bill Wallis
  Aug 27 at 10:52
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  It seems to me that := is introduced sometime later.
  – nmd_07
  Aug 27 at 10:53
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  In some programming languages like Go := used to define and assign, whereas = is for just assignment. Maybe this analogy help you
  – Grijesh Chauhan
  Aug 27 at 16:32
  

  
  
  
  

add a comment | 

up vote
7
down vote

favorite

2

up vote
7
down vote

favorite

2

2

This question already has an answer here:

• 
  Difference between $:=$ and $=$
  
  3 answers
  
  

I see two kinds of equal signs in different resources in regards to defining sets. One is := and the other is =

An example : S = 1, 2, 3 or S := 1, 2, 3

I realized that resources concerned with mathematical analysis uses the latter whereas others use the former.

Is there any difference in the meaning of both notations?

elementary-set-theory notation

share|cite|improve this question

edited Aug 27 at 11:06

Brahadeesh

4,12331550

asked Aug 27 at 10:51

nmd_07

506

This question already has an answer here:

• 
  Difference between $:=$ and $=$
  
  3 answers
  
  

I see two kinds of equal signs in different resources in regards to defining sets. One is := and the other is =

An example : S = 1, 2, 3 or S := 1, 2, 3

I realized that resources concerned with mathematical analysis uses the latter whereas others use the former.

Is there any difference in the meaning of both notations?

This question already has an answer here:

• 
  Difference between $:=$ and $=$
  
  3 answers
  
  

elementary-set-theory notation

share|cite|improve this question

edited Aug 27 at 11:06

Brahadeesh

4,12331550

asked Aug 27 at 10:51

nmd_07

506

share|cite|improve this question

share|cite|improve this question

edited Aug 27 at 11:06

Brahadeesh

4,12331550

edited Aug 27 at 11:06

Brahadeesh

4,12331550

edited Aug 27 at 11:06

Brahadeesh

4,12331550

4,12331550

asked Aug 27 at 10:51

nmd_07

506

asked Aug 27 at 10:51

nmd_07

506

asked Aug 27 at 10:51

nmd_07

506

506

marked as duplicate by Carsten S, BlueRaja - Danny Pflughoeft, quid♦ Aug 27 at 17:15

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

marked as duplicate by Carsten S, BlueRaja - Danny Pflughoeft, quid♦ Aug 27 at 17:15

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  The := symbol is usually 'defined as', rather than 'equal to'.
  – Bill Wallis
  Aug 27 at 10:52
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  It seems to me that := is introduced sometime later.
  – nmd_07
  Aug 27 at 10:53
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  In some programming languages like Go := used to define and assign, whereas = is for just assignment. Maybe this analogy help you
  – Grijesh Chauhan
  Aug 27 at 16:32
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  The := symbol is usually 'defined as', rather than 'equal to'.
  – Bill Wallis
  Aug 27 at 10:52
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  It seems to me that := is introduced sometime later.
  – nmd_07
  Aug 27 at 10:53
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  In some programming languages like Go := used to define and assign, whereas = is for just assignment. Maybe this analogy help you
  – Grijesh Chauhan
  Aug 27 at 16:32
  

  
  
  
  

2

2

The := symbol is usually 'defined as', rather than 'equal to'.
– Bill Wallis
Aug 27 at 10:52

The := symbol is usually 'defined as', rather than 'equal to'.
– Bill Wallis
Aug 27 at 10:52

It seems to me that := is introduced sometime later.
– nmd_07
Aug 27 at 10:53

It seems to me that := is introduced sometime later.
– nmd_07
Aug 27 at 10:53

In some programming languages like Go := used to define and assign, whereas = is for just assignment. Maybe this analogy help you
– Grijesh Chauhan
Aug 27 at 16:32

In some programming languages like Go := used to define and assign, whereas = is for just assignment. Maybe this analogy help you
– Grijesh Chauhan
Aug 27 at 16:32

add a comment | 

3 Answers
3

active

oldest

votes

up vote
4
down vote



accepted

The symbol "$:=$" seems to have been introduced in programming languages in the 1960's. For instance in Pascal, one writes $x = 0$ for testing equality (like in "if $x=0$ then...") and $x := 0$ to assign the value $0$ to the variable $x$.

However, since assignment is more frequent than equality testing, languages like C or Java use a different syntax: $x = 0$ for assignment and $x == 0$ for equality testing.

After that, the notation $:=$ spread out in mathematical writing, mostly to mean "equal by definition". I would not recommend using it, but it is nevertheless quite common.

EDIT. According to the Wikipedia entry ALGOL 58, ALGOL 58, originally known as IAL, is one of the family of ALGOL computer programming languages.

The distinction between assignment (:= representing a left-facing
arrow) and the equality relation (=) was introduced in IAL and kept in
ALGOL 60.

Thus the use of := in computer science goes back to at least 1958.

share|cite|improve this answer

edited Aug 27 at 16:34

answered Aug 27 at 13:15

J.-E. Pin

17.4k21753

• 
  
  
  

  
  5
  

  
  
  
  
  
  

  
  Would you have a citation for that? I always assumed that Pascal etc. used := because that was already used in maths.
  – leftaroundabout
  Aug 27 at 13:40
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  := is also discouraged by Milne. (Who, incidentally, also considers it a programming jargon. FWIW, the idea that it came first in mathematical writing sounds bizarre to me.)
  – Emil Jeřábek
  Aug 27 at 15:05
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  If $:=$ came from math first then all programing languages would use it. Many use $=$ to assign ($:=$) and $==$ to test equality ($=$). Thing is, math doesn't need two notations; being equal is the only concern and whether their equal because they just are or we defined them to be is not a high concept worth considering. But in programming the two concepts are essential. You can't start a program if you can't give things values! So if such a distinction didn't exist, programmers would have to invent one.
  – fleablood
  Aug 27 at 16:09
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  For what it's worth, I had never seen $:=$ in mathematics until three years ago.
  – fleablood
  Aug 27 at 16:10
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @fleablood: I haven't seen it in pure mathematical contexts either, but I've come across it several times in physics. As far as I can tell, it entered the programming-language tradition with the Algol committee, whose members were interested in scientific computing (Naur, the editor of the Algol 60 report, was originally an astronomer).
  – Henning Makholm
  Aug 27 at 19:31
  

  
  
  
  

 | 
show 1 more comment

up vote
10
down vote

There's not a lot of difference :)

$:=$ means "is defined to equal" and is most often used to say that the Right Hand Side is formally defining the Left Hand Side.

"=" is equals and can also be used to define things (though I, personally, would consider it a little bit loose) but can also be used to state that the Left Hand Side and the Right Hand Side are the same, though one or both may have come from a different definition.

share|cite|improve this answer

answered Aug 27 at 10:54

postmortes

1,56311016

add a comment | 

up vote
6
down vote

The symbol "$:=$" is used when you define something to be equal to something. For example, the rationals $mathbbQ:=Q(mathbbZ)$ are defined the field of fractions of the integers. If someone showed you that symbol, you would not have knew what it is. It's just defined as that.

The symbol "$=$" means equality that arises from something.

share|cite|improve this answer

answered Aug 27 at 11:01

Mario 04

120113

add a comment | 

3 Answers
3

active

oldest

votes

3 Answers
3

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
4
down vote



accepted

The symbol "$:=$" seems to have been introduced in programming languages in the 1960's. For instance in Pascal, one writes $x = 0$ for testing equality (like in "if $x=0$ then...") and $x := 0$ to assign the value $0$ to the variable $x$.

However, since assignment is more frequent than equality testing, languages like C or Java use a different syntax: $x = 0$ for assignment and $x == 0$ for equality testing.

After that, the notation $:=$ spread out in mathematical writing, mostly to mean "equal by definition". I would not recommend using it, but it is nevertheless quite common.

EDIT. According to the Wikipedia entry ALGOL 58, ALGOL 58, originally known as IAL, is one of the family of ALGOL computer programming languages.

The distinction between assignment (:= representing a left-facing
arrow) and the equality relation (=) was introduced in IAL and kept in
ALGOL 60.

Thus the use of := in computer science goes back to at least 1958.

share|cite|improve this answer

edited Aug 27 at 16:34

answered Aug 27 at 13:15

J.-E. Pin

17.4k21753

• 
  
  
  

  
  5
  

  
  
  
  
  
  

  
  Would you have a citation for that? I always assumed that Pascal etc. used := because that was already used in maths.
  – leftaroundabout
  Aug 27 at 13:40
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  := is also discouraged by Milne. (Who, incidentally, also considers it a programming jargon. FWIW, the idea that it came first in mathematical writing sounds bizarre to me.)
  – Emil Jeřábek
  Aug 27 at 15:05
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  If $:=$ came from math first then all programing languages would use it. Many use $=$ to assign ($:=$) and $==$ to test equality ($=$). Thing is, math doesn't need two notations; being equal is the only concern and whether their equal because they just are or we defined them to be is not a high concept worth considering. But in programming the two concepts are essential. You can't start a program if you can't give things values! So if such a distinction didn't exist, programmers would have to invent one.
  – fleablood
  Aug 27 at 16:09
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  For what it's worth, I had never seen $:=$ in mathematics until three years ago.
  – fleablood
  Aug 27 at 16:10
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @fleablood: I haven't seen it in pure mathematical contexts either, but I've come across it several times in physics. As far as I can tell, it entered the programming-language tradition with the Algol committee, whose members were interested in scientific computing (Naur, the editor of the Algol 60 report, was originally an astronomer).
  – Henning Makholm
  Aug 27 at 19:31
  

  
  
  
  

 | 
show 1 more comment

up vote
4
down vote



accepted

The symbol "$:=$" seems to have been introduced in programming languages in the 1960's. For instance in Pascal, one writes $x = 0$ for testing equality (like in "if $x=0$ then...") and $x := 0$ to assign the value $0$ to the variable $x$.

However, since assignment is more frequent than equality testing, languages like C or Java use a different syntax: $x = 0$ for assignment and $x == 0$ for equality testing.

After that, the notation $:=$ spread out in mathematical writing, mostly to mean "equal by definition". I would not recommend using it, but it is nevertheless quite common.

EDIT. According to the Wikipedia entry ALGOL 58, ALGOL 58, originally known as IAL, is one of the family of ALGOL computer programming languages.

The distinction between assignment (:= representing a left-facing
arrow) and the equality relation (=) was introduced in IAL and kept in
ALGOL 60.

Thus the use of := in computer science goes back to at least 1958.

share|cite|improve this answer

edited Aug 27 at 16:34

answered Aug 27 at 13:15

J.-E. Pin

17.4k21753

• 
  
  
  

  
  5
  

  
  
  
  
  
  

  
  Would you have a citation for that? I always assumed that Pascal etc. used := because that was already used in maths.
  – leftaroundabout
  Aug 27 at 13:40
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  := is also discouraged by Milne. (Who, incidentally, also considers it a programming jargon. FWIW, the idea that it came first in mathematical writing sounds bizarre to me.)
  – Emil Jeřábek
  Aug 27 at 15:05
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  If $:=$ came from math first then all programing languages would use it. Many use $=$ to assign ($:=$) and $==$ to test equality ($=$). Thing is, math doesn't need two notations; being equal is the only concern and whether their equal because they just are or we defined them to be is not a high concept worth considering. But in programming the two concepts are essential. You can't start a program if you can't give things values! So if such a distinction didn't exist, programmers would have to invent one.
  – fleablood
  Aug 27 at 16:09
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  For what it's worth, I had never seen $:=$ in mathematics until three years ago.
  – fleablood
  Aug 27 at 16:10
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @fleablood: I haven't seen it in pure mathematical contexts either, but I've come across it several times in physics. As far as I can tell, it entered the programming-language tradition with the Algol committee, whose members were interested in scientific computing (Naur, the editor of the Algol 60 report, was originally an astronomer).
  – Henning Makholm
  Aug 27 at 19:31
  

  
  
  
  

 | 
show 1 more comment

up vote
4
down vote



accepted

up vote
4
down vote



accepted

The symbol "$:=$" seems to have been introduced in programming languages in the 1960's. For instance in Pascal, one writes $x = 0$ for testing equality (like in "if $x=0$ then...") and $x := 0$ to assign the value $0$ to the variable $x$.

However, since assignment is more frequent than equality testing, languages like C or Java use a different syntax: $x = 0$ for assignment and $x == 0$ for equality testing.

After that, the notation $:=$ spread out in mathematical writing, mostly to mean "equal by definition". I would not recommend using it, but it is nevertheless quite common.

EDIT. According to the Wikipedia entry ALGOL 58, ALGOL 58, originally known as IAL, is one of the family of ALGOL computer programming languages.

The distinction between assignment (:= representing a left-facing
arrow) and the equality relation (=) was introduced in IAL and kept in
ALGOL 60.

Thus the use of := in computer science goes back to at least 1958.

share|cite|improve this answer

edited Aug 27 at 16:34

answered Aug 27 at 13:15

J.-E. Pin

17.4k21753

The symbol "$:=$" seems to have been introduced in programming languages in the 1960's. For instance in Pascal, one writes $x = 0$ for testing equality (like in "if $x=0$ then...") and $x := 0$ to assign the value $0$ to the variable $x$.

However, since assignment is more frequent than equality testing, languages like C or Java use a different syntax: $x = 0$ for assignment and $x == 0$ for equality testing.

After that, the notation $:=$ spread out in mathematical writing, mostly to mean "equal by definition". I would not recommend using it, but it is nevertheless quite common.

EDIT. According to the Wikipedia entry ALGOL 58, ALGOL 58, originally known as IAL, is one of the family of ALGOL computer programming languages.

The distinction between assignment (:= representing a left-facing
arrow) and the equality relation (=) was introduced in IAL and kept in
ALGOL 60.

Thus the use of := in computer science goes back to at least 1958.

share|cite|improve this answer

edited Aug 27 at 16:34

answered Aug 27 at 13:15

J.-E. Pin

17.4k21753

share|cite|improve this answer

share|cite|improve this answer

edited Aug 27 at 16:34

edited Aug 27 at 16:34

edited Aug 27 at 16:34

answered Aug 27 at 13:15

J.-E. Pin

17.4k21753

answered Aug 27 at 13:15

J.-E. Pin

17.4k21753

answered Aug 27 at 13:15

J.-E. Pin

17.4k21753

17.4k21753

• 
  
  
  

  
  5
  

  
  
  
  
  
  

  
  Would you have a citation for that? I always assumed that Pascal etc. used := because that was already used in maths.
  – leftaroundabout
  Aug 27 at 13:40
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  := is also discouraged by Milne. (Who, incidentally, also considers it a programming jargon. FWIW, the idea that it came first in mathematical writing sounds bizarre to me.)
  – Emil Jeřábek
  Aug 27 at 15:05
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  If $:=$ came from math first then all programing languages would use it. Many use $=$ to assign ($:=$) and $==$ to test equality ($=$). Thing is, math doesn't need two notations; being equal is the only concern and whether their equal because they just are or we defined them to be is not a high concept worth considering. But in programming the two concepts are essential. You can't start a program if you can't give things values! So if such a distinction didn't exist, programmers would have to invent one.
  – fleablood
  Aug 27 at 16:09
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  For what it's worth, I had never seen $:=$ in mathematics until three years ago.
  – fleablood
  Aug 27 at 16:10
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @fleablood: I haven't seen it in pure mathematical contexts either, but I've come across it several times in physics. As far as I can tell, it entered the programming-language tradition with the Algol committee, whose members were interested in scientific computing (Naur, the editor of the Algol 60 report, was originally an astronomer).
  – Henning Makholm
  Aug 27 at 19:31
  

  
  
  
  

 | 
show 1 more comment

• 
  
  
  

  
  5
  

  
  
  
  
  
  

  
  Would you have a citation for that? I always assumed that Pascal etc. used := because that was already used in maths.
  – leftaroundabout
  Aug 27 at 13:40
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  := is also discouraged by Milne. (Who, incidentally, also considers it a programming jargon. FWIW, the idea that it came first in mathematical writing sounds bizarre to me.)
  – Emil Jeřábek
  Aug 27 at 15:05
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  If $:=$ came from math first then all programing languages would use it. Many use $=$ to assign ($:=$) and $==$ to test equality ($=$). Thing is, math doesn't need two notations; being equal is the only concern and whether their equal because they just are or we defined them to be is not a high concept worth considering. But in programming the two concepts are essential. You can't start a program if you can't give things values! So if such a distinction didn't exist, programmers would have to invent one.
  – fleablood
  Aug 27 at 16:09
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  For what it's worth, I had never seen $:=$ in mathematics until three years ago.
  – fleablood
  Aug 27 at 16:10
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @fleablood: I haven't seen it in pure mathematical contexts either, but I've come across it several times in physics. As far as I can tell, it entered the programming-language tradition with the Algol committee, whose members were interested in scientific computing (Naur, the editor of the Algol 60 report, was originally an astronomer).
  – Henning Makholm
  Aug 27 at 19:31
  

  
  
  
  

5

5

Would you have a citation for that? I always assumed that Pascal etc. used := because that was already used in maths.
– leftaroundabout
Aug 27 at 13:40

Would you have a citation for that? I always assumed that Pascal etc. used := because that was already used in maths.
– leftaroundabout
Aug 27 at 13:40

:= is also discouraged by Milne. (Who, incidentally, also considers it a programming jargon. FWIW, the idea that it came first in mathematical writing sounds bizarre to me.)
– Emil Jeřábek
Aug 27 at 15:05

:= is also discouraged by Milne. (Who, incidentally, also considers it a programming jargon. FWIW, the idea that it came first in mathematical writing sounds bizarre to me.)
– Emil Jeřábek
Aug 27 at 15:05

If $:=$ came from math first then all programing languages would use it. Many use $=$ to assign ($:=$) and $==$ to test equality ($=$). Thing is, math doesn't need two notations; being equal is the only concern and whether their equal because they just are or we defined them to be is not a high concept worth considering. But in programming the two concepts are essential. You can't start a program if you can't give things values! So if such a distinction didn't exist, programmers would have to invent one.
– fleablood
Aug 27 at 16:09

If $:=$ came from math first then all programing languages would use it. Many use $=$ to assign ($:=$) and $==$ to test equality ($=$). Thing is, math doesn't need two notations; being equal is the only concern and whether their equal because they just are or we defined them to be is not a high concept worth considering. But in programming the two concepts are essential. You can't start a program if you can't give things values! So if such a distinction didn't exist, programmers would have to invent one.
– fleablood
Aug 27 at 16:09

For what it's worth, I had never seen $:=$ in mathematics until three years ago.
– fleablood
Aug 27 at 16:10

For what it's worth, I had never seen $:=$ in mathematics until three years ago.
– fleablood
Aug 27 at 16:10

@fleablood: I haven't seen it in pure mathematical contexts either, but I've come across it several times in physics. As far as I can tell, it entered the programming-language tradition with the Algol committee, whose members were interested in scientific computing (Naur, the editor of the Algol 60 report, was originally an astronomer).
– Henning Makholm
Aug 27 at 19:31

@fleablood: I haven't seen it in pure mathematical contexts either, but I've come across it several times in physics. As far as I can tell, it entered the programming-language tradition with the Algol committee, whose members were interested in scientific computing (Naur, the editor of the Algol 60 report, was originally an astronomer).
– Henning Makholm
Aug 27 at 19:31

 | 
show 1 more comment

up vote
10
down vote

There's not a lot of difference :)

$:=$ means "is defined to equal" and is most often used to say that the Right Hand Side is formally defining the Left Hand Side.

"=" is equals and can also be used to define things (though I, personally, would consider it a little bit loose) but can also be used to state that the Left Hand Side and the Right Hand Side are the same, though one or both may have come from a different definition.

share|cite|improve this answer

answered Aug 27 at 10:54

postmortes

1,56311016

add a comment | 

up vote
10
down vote

There's not a lot of difference :)

$:=$ means "is defined to equal" and is most often used to say that the Right Hand Side is formally defining the Left Hand Side.

"=" is equals and can also be used to define things (though I, personally, would consider it a little bit loose) but can also be used to state that the Left Hand Side and the Right Hand Side are the same, though one or both may have come from a different definition.

share|cite|improve this answer

answered Aug 27 at 10:54

postmortes

1,56311016

add a comment | 

up vote
10
down vote

up vote
10
down vote

There's not a lot of difference :)

$:=$ means "is defined to equal" and is most often used to say that the Right Hand Side is formally defining the Left Hand Side.

"=" is equals and can also be used to define things (though I, personally, would consider it a little bit loose) but can also be used to state that the Left Hand Side and the Right Hand Side are the same, though one or both may have come from a different definition.

share|cite|improve this answer

answered Aug 27 at 10:54

postmortes

1,56311016

There's not a lot of difference :)

$:=$ means "is defined to equal" and is most often used to say that the Right Hand Side is formally defining the Left Hand Side.

"=" is equals and can also be used to define things (though I, personally, would consider it a little bit loose) but can also be used to state that the Left Hand Side and the Right Hand Side are the same, though one or both may have come from a different definition.

share|cite|improve this answer

answered Aug 27 at 10:54

postmortes

1,56311016

share|cite|improve this answer

share|cite|improve this answer

answered Aug 27 at 10:54

postmortes

1,56311016

answered Aug 27 at 10:54

postmortes

1,56311016

answered Aug 27 at 10:54

postmortes

1,56311016

1,56311016

add a comment | 

add a comment | 

up vote
6
down vote

The symbol "$:=$" is used when you define something to be equal to something. For example, the rationals $mathbbQ:=Q(mathbbZ)$ are defined the field of fractions of the integers. If someone showed you that symbol, you would not have knew what it is. It's just defined as that.

The symbol "$=$" means equality that arises from something.

share|cite|improve this answer

answered Aug 27 at 11:01

Mario 04

120113

add a comment | 

up vote
6
down vote

The symbol "$:=$" is used when you define something to be equal to something. For example, the rationals $mathbbQ:=Q(mathbbZ)$ are defined the field of fractions of the integers. If someone showed you that symbol, you would not have knew what it is. It's just defined as that.

The symbol "$=$" means equality that arises from something.

share|cite|improve this answer

answered Aug 27 at 11:01

Mario 04

120113

add a comment | 

up vote
6
down vote

up vote
6
down vote

The symbol "$:=$" is used when you define something to be equal to something. For example, the rationals $mathbbQ:=Q(mathbbZ)$ are defined the field of fractions of the integers. If someone showed you that symbol, you would not have knew what it is. It's just defined as that.

The symbol "$=$" means equality that arises from something.

share|cite|improve this answer

answered Aug 27 at 11:01

Mario 04

120113

The symbol "$:=$" is used when you define something to be equal to something. For example, the rationals $mathbbQ:=Q(mathbbZ)$ are defined the field of fractions of the integers. If someone showed you that symbol, you would not have knew what it is. It's just defined as that.

The symbol "$=$" means equality that arises from something.

share|cite|improve this answer

answered Aug 27 at 11:01

Mario 04

120113

share|cite|improve this answer

share|cite|improve this answer

answered Aug 27 at 11:01

Mario 04

120113

answered Aug 27 at 11:01

Mario 04

120113

answered Aug 27 at 11:01

Mario 04

120113

120113

add a comment | 

add a comment |