If only the second operand in addition is a string then the output is a string:
let a = 1 + '2';
console.log(typeof a); // string
And if, instead, only the first operand is a string, then the output is still a string:
let b = '1' + 2;
console.log(typeof b); // string
I was guessing that there would be some kind of argument precedence. Is there a reason why this mathematical function defaults to a non-numerical output with mixed-type arguments?
As it is often the case, the answer is "because the spec says so". More specifically, section 11.6.1 The Addition operator ( + ).
On step 7, you can read
If Type(lprim) is String or Type(rprim) is String, then
Return the String that is the result of concatenating ToString(lprim) followed by ToString(rprim)
In other words, if at least one of the operands is a string, the result will be the concatenation of the string representation of both operands.
There is precedence in a way, because if both operands were functions the left one would be evaluated before the right one, but it doesn't matter for the algorithm that decides if the + operation should return a string or a number.
Note: I referred to the ECMAScript 5 spec but you can find something equivalent in the newer versions.
When a single operator is part of an expression, the expression is performed left to right, but in JavaScript, if any one of the operands used with the + operator is a string, the other one will be converted to a string - it doesn't matter which one. This is because the + operation can mean string addition (concatenation) or mathematical addition. When one operand is a string, the JavaScript runtime correctly assumes that the + should mean string addition because the string could contain a non-numeric value and doing math with non-numeric values is problematic, to say the least.
You would need to do a conversion on the non-string before the concatenation occurs. This can be done in a number of ways:
console.log(1 + +"2"); // prepending a + to a string attempts to convert to a number
// Note that with all of the following there is a nested function call being performed
// and these functions take an argument, which requires () for the argument to be passed.
// Because of the nested (), that function call is performed first and the result of the
// function call is returned to the expression.
console.log(1 + parseInt("2.4")); // parse the integer portion of the string into a number
console.log(1 + parseFloat("2.4")); // parse the floating point number in the string into a number
console.log(1 + Number("2")); // convert the string into a number
The basic operator precedence is:
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
So, in the following examples, you can see that happening:
// Here, the order of operations will be:
// Parenthesis: (2/2) === 1
// Multiplication: 10 * 1 === 10
// Addition: 1 + 10 === 11
// Subtraction: 11 - 3 === 8
console.log(1 + 10 * (2 / 2) - 3);
// But here, because of the string, the order of operations will be:
// Parenthesis: (2/2) === 1
// Multiplication: 10 * 1 === 10
// Addition: "1" + 10 === "110" (one operand is a string, so the other converts to a string)
// Subtraction: "110" - 3 === 107 (the string "110" will be implicitly converted to a number
// becuase the - sign only has one meaning in a mathmatical
// expression)
console.log("1" + 10 * (2 / 2) - 3);
See JavaScript Operator Precedence for a full list of operators and their precedence.
See Unary + Operator for how it is used to convert to a number.
Also note that we're not talking about "arguments" here (an argument is what is passed to a method or function). These are operands in an expression with operators.
Related
I don't understand why JavaScript works this way.
console.log("1" + 1);
console.log("1" - 1);
The first line prints 11, and the second prints 0.
Why does JavaScript handle the first as a String and the second as a number?
String concatenation is done with + so Javascript will convert the first numeric 1 to a string and concatenate "1" and "1" making "11".
You cannot perform subtraction on strings, so Javascript converts the second "1" to a number and subtracts 1 from 1, resulting in zero.
+ is ambiguous. It can mean "concatenate" or "add". Since one side is a string, it is taken to mean "concatenate", hence the result is 11 (which, by the way, was one of my favourite jokes as a young child. That and "1 + 1 = window", as shown visually: │┼│ ニ ⊞)
- however has only one meaning: subtract. So it subtracts.
This kind of problem is not present in other languages such as PHP, where "concatenate" is . instead of +, making no ambiguity. Still other languages like MySQL don't even have a concatenation operator, instead using CONCAT(a,b,c...).
Because the spec explicitly tells to do so.
Page 75. Note the difference between 11.6.1 steps 5-8 and 11.6.2 steps 5-7.
11.6.1 - describes how addition operator works
1-4. ...
5. Let lprim be ToPrimitive(lval).
6. Let rprim be ToPrimitive(rval).
7. If Type(lprim) is String or Type(rprim) is String, then
7a. Return the String that is the result of concatenating ToString(lprim) followed by ToString(rprim)
8. Return the result of applying the addition operation to ToNumber(lprim) and ToNumber(rprim)
11.6.2 - describes how subtraction operator works
1-4. ...
5. Let lnum be ToNumber(lval).
6. Let rnum be ToNumber(rval).
7. Return the result of applying the subtraction operation to lnum and rnum
Summary
In case of addition if any of the operands when converted to primitive value without any hints suddenly becomes a string the second one is converted to a string too. In case of subtraction both operands are converted to a number.
There is no dedicated string concatenation operator in JavaScript**. The addition operator + performs either string concatenation or addition, depending on the type of operands:
"1" + 1 // "11"
1 + "1" // "11"
1 + 1 // 2
There is no opposite of concatenation (I think) and the subtraction operator - only performs subtraction regardless of the type of operands:
"1" - 1 // 0
1 - "1" // 0
1 - 1 // 0
"a" - 1 // NaN
** The . operator in PHP and & operator in VB are dedicated string concatenation operators.
+ is both an addition operator for numeric variables, and a concatenation operator for strings.
Whenever there's a string after a +, Javascript will choose to use the + as a concatenation operator and convert (typed) as many terms as possible around the string so it can concatenate them. That's just the behaviour of Javascript. (If you tried console.log(23 + 2 + "." + 1 + 5 + "02" + 02);, you'll get the result 25.15022. The number 02 was typed into the string 2 before being concatenated.
- can only be a subtraction operator, so when given a string, it will implicitly change the type of the string "1" into a numeric 1; if it didn't do that, there's no way "1" - 1 would make sense. If you tried console.log(23 + 2 + 1 + 5 - "02" + 03); you'll get 32 - the string 02 gets converted into the number 2. The term after the - must be able to be converted into a number; if you tried console.log(23 - 2 - "." - 1 - 5 - 02 - "02"); you'll get NaN returned.
More importantly, if you tried console.log(23 + 2 + "." + 1 + 5 - "02" + 03);, it will output 26.15, where everything before - was treated as a string (because it contains a string ".", and then the term after the - is treated as a number.
According to the standard EcmaScript 262. The + and - operators behave differently when strings are involved. The first converts every value to a string. The second converts every value to a number.
From the standard:
If Type(lprim) is String or Type(rprim) is String, then Return the
String that is the result of concatenating ToString(lprim) followed by
ToString(rprim)
This rules implies that if in the expression there is a string value, all values involved in the + operation are converted to a string. In JavaScript when the + operator is used with strings, it concatenates them. This is why console.log("5"+1) returns "51". 1 is converted to a string and then, "5" + "1" are concatenated together.
Nevertheless, the above rule doesn't apply for the - operator. When you are using a - all values are converted to numbers according to the Standard (see below). Therefore, in this case, "5" is converted to 5 and then 1 is subtracted.
From the standard:
5 Let lnum be ToNumber(lval).
6 Let rnum be ToNumber(rval).
Operator definition from the standard EcmaScript 262.
Operator + : http://www.ecma-international.org/ecma-262/5.1/#sec-11.6.1
Operator - : http://www.ecma-international.org/ecma-262/5.1/#sec-11.6.2
Using plus and a string "" you basically return a string because you are performing a concatenation:
typeof ("" + 1 + 0) // string
typeof (1 + 0) // number
When using - instead you convert to a number as string concatenation is possible:
typeof ("" - 1 + 0) // number
I don't understand why JavaScript works this way.
console.log("1" + 1);
console.log("1" - 1);
The first line prints 11, and the second prints 0.
Why does JavaScript handle the first as a String and the second as a number?
String concatenation is done with + so Javascript will convert the first numeric 1 to a string and concatenate "1" and "1" making "11".
You cannot perform subtraction on strings, so Javascript converts the second "1" to a number and subtracts 1 from 1, resulting in zero.
+ is ambiguous. It can mean "concatenate" or "add". Since one side is a string, it is taken to mean "concatenate", hence the result is 11 (which, by the way, was one of my favourite jokes as a young child. That and "1 + 1 = window", as shown visually: │┼│ ニ ⊞)
- however has only one meaning: subtract. So it subtracts.
This kind of problem is not present in other languages such as PHP, where "concatenate" is . instead of +, making no ambiguity. Still other languages like MySQL don't even have a concatenation operator, instead using CONCAT(a,b,c...).
Because the spec explicitly tells to do so.
Page 75. Note the difference between 11.6.1 steps 5-8 and 11.6.2 steps 5-7.
11.6.1 - describes how addition operator works
1-4. ...
5. Let lprim be ToPrimitive(lval).
6. Let rprim be ToPrimitive(rval).
7. If Type(lprim) is String or Type(rprim) is String, then
7a. Return the String that is the result of concatenating ToString(lprim) followed by ToString(rprim)
8. Return the result of applying the addition operation to ToNumber(lprim) and ToNumber(rprim)
11.6.2 - describes how subtraction operator works
1-4. ...
5. Let lnum be ToNumber(lval).
6. Let rnum be ToNumber(rval).
7. Return the result of applying the subtraction operation to lnum and rnum
Summary
In case of addition if any of the operands when converted to primitive value without any hints suddenly becomes a string the second one is converted to a string too. In case of subtraction both operands are converted to a number.
There is no dedicated string concatenation operator in JavaScript**. The addition operator + performs either string concatenation or addition, depending on the type of operands:
"1" + 1 // "11"
1 + "1" // "11"
1 + 1 // 2
There is no opposite of concatenation (I think) and the subtraction operator - only performs subtraction regardless of the type of operands:
"1" - 1 // 0
1 - "1" // 0
1 - 1 // 0
"a" - 1 // NaN
** The . operator in PHP and & operator in VB are dedicated string concatenation operators.
+ is both an addition operator for numeric variables, and a concatenation operator for strings.
Whenever there's a string after a +, Javascript will choose to use the + as a concatenation operator and convert (typed) as many terms as possible around the string so it can concatenate them. That's just the behaviour of Javascript. (If you tried console.log(23 + 2 + "." + 1 + 5 + "02" + 02);, you'll get the result 25.15022. The number 02 was typed into the string 2 before being concatenated.
- can only be a subtraction operator, so when given a string, it will implicitly change the type of the string "1" into a numeric 1; if it didn't do that, there's no way "1" - 1 would make sense. If you tried console.log(23 + 2 + 1 + 5 - "02" + 03); you'll get 32 - the string 02 gets converted into the number 2. The term after the - must be able to be converted into a number; if you tried console.log(23 - 2 - "." - 1 - 5 - 02 - "02"); you'll get NaN returned.
More importantly, if you tried console.log(23 + 2 + "." + 1 + 5 - "02" + 03);, it will output 26.15, where everything before - was treated as a string (because it contains a string ".", and then the term after the - is treated as a number.
According to the standard EcmaScript 262. The + and - operators behave differently when strings are involved. The first converts every value to a string. The second converts every value to a number.
From the standard:
If Type(lprim) is String or Type(rprim) is String, then Return the
String that is the result of concatenating ToString(lprim) followed by
ToString(rprim)
This rules implies that if in the expression there is a string value, all values involved in the + operation are converted to a string. In JavaScript when the + operator is used with strings, it concatenates them. This is why console.log("5"+1) returns "51". 1 is converted to a string and then, "5" + "1" are concatenated together.
Nevertheless, the above rule doesn't apply for the - operator. When you are using a - all values are converted to numbers according to the Standard (see below). Therefore, in this case, "5" is converted to 5 and then 1 is subtracted.
From the standard:
5 Let lnum be ToNumber(lval).
6 Let rnum be ToNumber(rval).
Operator definition from the standard EcmaScript 262.
Operator + : http://www.ecma-international.org/ecma-262/5.1/#sec-11.6.1
Operator - : http://www.ecma-international.org/ecma-262/5.1/#sec-11.6.2
Using plus and a string "" you basically return a string because you are performing a concatenation:
typeof ("" + 1 + 0) // string
typeof (1 + 0) // number
When using - instead you convert to a number as string concatenation is possible:
typeof ("" - 1 + 0) // number
I don't understand why JavaScript works this way.
console.log("1" + 1);
console.log("1" - 1);
The first line prints 11, and the second prints 0.
Why does JavaScript handle the first as a String and the second as a number?
String concatenation is done with + so Javascript will convert the first numeric 1 to a string and concatenate "1" and "1" making "11".
You cannot perform subtraction on strings, so Javascript converts the second "1" to a number and subtracts 1 from 1, resulting in zero.
+ is ambiguous. It can mean "concatenate" or "add". Since one side is a string, it is taken to mean "concatenate", hence the result is 11 (which, by the way, was one of my favourite jokes as a young child. That and "1 + 1 = window", as shown visually: │┼│ ニ ⊞)
- however has only one meaning: subtract. So it subtracts.
This kind of problem is not present in other languages such as PHP, where "concatenate" is . instead of +, making no ambiguity. Still other languages like MySQL don't even have a concatenation operator, instead using CONCAT(a,b,c...).
Because the spec explicitly tells to do so.
Page 75. Note the difference between 11.6.1 steps 5-8 and 11.6.2 steps 5-7.
11.6.1 - describes how addition operator works
1-4. ...
5. Let lprim be ToPrimitive(lval).
6. Let rprim be ToPrimitive(rval).
7. If Type(lprim) is String or Type(rprim) is String, then
7a. Return the String that is the result of concatenating ToString(lprim) followed by ToString(rprim)
8. Return the result of applying the addition operation to ToNumber(lprim) and ToNumber(rprim)
11.6.2 - describes how subtraction operator works
1-4. ...
5. Let lnum be ToNumber(lval).
6. Let rnum be ToNumber(rval).
7. Return the result of applying the subtraction operation to lnum and rnum
Summary
In case of addition if any of the operands when converted to primitive value without any hints suddenly becomes a string the second one is converted to a string too. In case of subtraction both operands are converted to a number.
There is no dedicated string concatenation operator in JavaScript**. The addition operator + performs either string concatenation or addition, depending on the type of operands:
"1" + 1 // "11"
1 + "1" // "11"
1 + 1 // 2
There is no opposite of concatenation (I think) and the subtraction operator - only performs subtraction regardless of the type of operands:
"1" - 1 // 0
1 - "1" // 0
1 - 1 // 0
"a" - 1 // NaN
** The . operator in PHP and & operator in VB are dedicated string concatenation operators.
+ is both an addition operator for numeric variables, and a concatenation operator for strings.
Whenever there's a string after a +, Javascript will choose to use the + as a concatenation operator and convert (typed) as many terms as possible around the string so it can concatenate them. That's just the behaviour of Javascript. (If you tried console.log(23 + 2 + "." + 1 + 5 + "02" + 02);, you'll get the result 25.15022. The number 02 was typed into the string 2 before being concatenated.
- can only be a subtraction operator, so when given a string, it will implicitly change the type of the string "1" into a numeric 1; if it didn't do that, there's no way "1" - 1 would make sense. If you tried console.log(23 + 2 + 1 + 5 - "02" + 03); you'll get 32 - the string 02 gets converted into the number 2. The term after the - must be able to be converted into a number; if you tried console.log(23 - 2 - "." - 1 - 5 - 02 - "02"); you'll get NaN returned.
More importantly, if you tried console.log(23 + 2 + "." + 1 + 5 - "02" + 03);, it will output 26.15, where everything before - was treated as a string (because it contains a string ".", and then the term after the - is treated as a number.
According to the standard EcmaScript 262. The + and - operators behave differently when strings are involved. The first converts every value to a string. The second converts every value to a number.
From the standard:
If Type(lprim) is String or Type(rprim) is String, then Return the
String that is the result of concatenating ToString(lprim) followed by
ToString(rprim)
This rules implies that if in the expression there is a string value, all values involved in the + operation are converted to a string. In JavaScript when the + operator is used with strings, it concatenates them. This is why console.log("5"+1) returns "51". 1 is converted to a string and then, "5" + "1" are concatenated together.
Nevertheless, the above rule doesn't apply for the - operator. When you are using a - all values are converted to numbers according to the Standard (see below). Therefore, in this case, "5" is converted to 5 and then 1 is subtracted.
From the standard:
5 Let lnum be ToNumber(lval).
6 Let rnum be ToNumber(rval).
Operator definition from the standard EcmaScript 262.
Operator + : http://www.ecma-international.org/ecma-262/5.1/#sec-11.6.1
Operator - : http://www.ecma-international.org/ecma-262/5.1/#sec-11.6.2
Using plus and a string "" you basically return a string because you are performing a concatenation:
typeof ("" + 1 + 0) // string
typeof (1 + 0) // number
When using - instead you convert to a number as string concatenation is possible:
typeof ("" - 1 + 0) // number
I don't understand why JavaScript works this way.
console.log("1" + 1);
console.log("1" - 1);
The first line prints 11, and the second prints 0.
Why does JavaScript handle the first as a String and the second as a number?
String concatenation is done with + so Javascript will convert the first numeric 1 to a string and concatenate "1" and "1" making "11".
You cannot perform subtraction on strings, so Javascript converts the second "1" to a number and subtracts 1 from 1, resulting in zero.
+ is ambiguous. It can mean "concatenate" or "add". Since one side is a string, it is taken to mean "concatenate", hence the result is 11 (which, by the way, was one of my favourite jokes as a young child. That and "1 + 1 = window", as shown visually: │┼│ ニ ⊞)
- however has only one meaning: subtract. So it subtracts.
This kind of problem is not present in other languages such as PHP, where "concatenate" is . instead of +, making no ambiguity. Still other languages like MySQL don't even have a concatenation operator, instead using CONCAT(a,b,c...).
Because the spec explicitly tells to do so.
Page 75. Note the difference between 11.6.1 steps 5-8 and 11.6.2 steps 5-7.
11.6.1 - describes how addition operator works
1-4. ...
5. Let lprim be ToPrimitive(lval).
6. Let rprim be ToPrimitive(rval).
7. If Type(lprim) is String or Type(rprim) is String, then
7a. Return the String that is the result of concatenating ToString(lprim) followed by ToString(rprim)
8. Return the result of applying the addition operation to ToNumber(lprim) and ToNumber(rprim)
11.6.2 - describes how subtraction operator works
1-4. ...
5. Let lnum be ToNumber(lval).
6. Let rnum be ToNumber(rval).
7. Return the result of applying the subtraction operation to lnum and rnum
Summary
In case of addition if any of the operands when converted to primitive value without any hints suddenly becomes a string the second one is converted to a string too. In case of subtraction both operands are converted to a number.
There is no dedicated string concatenation operator in JavaScript**. The addition operator + performs either string concatenation or addition, depending on the type of operands:
"1" + 1 // "11"
1 + "1" // "11"
1 + 1 // 2
There is no opposite of concatenation (I think) and the subtraction operator - only performs subtraction regardless of the type of operands:
"1" - 1 // 0
1 - "1" // 0
1 - 1 // 0
"a" - 1 // NaN
** The . operator in PHP and & operator in VB are dedicated string concatenation operators.
+ is both an addition operator for numeric variables, and a concatenation operator for strings.
Whenever there's a string after a +, Javascript will choose to use the + as a concatenation operator and convert (typed) as many terms as possible around the string so it can concatenate them. That's just the behaviour of Javascript. (If you tried console.log(23 + 2 + "." + 1 + 5 + "02" + 02);, you'll get the result 25.15022. The number 02 was typed into the string 2 before being concatenated.
- can only be a subtraction operator, so when given a string, it will implicitly change the type of the string "1" into a numeric 1; if it didn't do that, there's no way "1" - 1 would make sense. If you tried console.log(23 + 2 + 1 + 5 - "02" + 03); you'll get 32 - the string 02 gets converted into the number 2. The term after the - must be able to be converted into a number; if you tried console.log(23 - 2 - "." - 1 - 5 - 02 - "02"); you'll get NaN returned.
More importantly, if you tried console.log(23 + 2 + "." + 1 + 5 - "02" + 03);, it will output 26.15, where everything before - was treated as a string (because it contains a string ".", and then the term after the - is treated as a number.
According to the standard EcmaScript 262. The + and - operators behave differently when strings are involved. The first converts every value to a string. The second converts every value to a number.
From the standard:
If Type(lprim) is String or Type(rprim) is String, then Return the
String that is the result of concatenating ToString(lprim) followed by
ToString(rprim)
This rules implies that if in the expression there is a string value, all values involved in the + operation are converted to a string. In JavaScript when the + operator is used with strings, it concatenates them. This is why console.log("5"+1) returns "51". 1 is converted to a string and then, "5" + "1" are concatenated together.
Nevertheless, the above rule doesn't apply for the - operator. When you are using a - all values are converted to numbers according to the Standard (see below). Therefore, in this case, "5" is converted to 5 and then 1 is subtracted.
From the standard:
5 Let lnum be ToNumber(lval).
6 Let rnum be ToNumber(rval).
Operator definition from the standard EcmaScript 262.
Operator + : http://www.ecma-international.org/ecma-262/5.1/#sec-11.6.1
Operator - : http://www.ecma-international.org/ecma-262/5.1/#sec-11.6.2
Using plus and a string "" you basically return a string because you are performing a concatenation:
typeof ("" + 1 + 0) // string
typeof (1 + 0) // number
When using - instead you convert to a number as string concatenation is possible:
typeof ("" - 1 + 0) // number
I don't understand why JavaScript works this way.
console.log("1" + 1);
console.log("1" - 1);
The first line prints 11, and the second prints 0.
Why does JavaScript handle the first as a String and the second as a number?
String concatenation is done with + so Javascript will convert the first numeric 1 to a string and concatenate "1" and "1" making "11".
You cannot perform subtraction on strings, so Javascript converts the second "1" to a number and subtracts 1 from 1, resulting in zero.
+ is ambiguous. It can mean "concatenate" or "add". Since one side is a string, it is taken to mean "concatenate", hence the result is 11 (which, by the way, was one of my favourite jokes as a young child. That and "1 + 1 = window", as shown visually: │┼│ ニ ⊞)
- however has only one meaning: subtract. So it subtracts.
This kind of problem is not present in other languages such as PHP, where "concatenate" is . instead of +, making no ambiguity. Still other languages like MySQL don't even have a concatenation operator, instead using CONCAT(a,b,c...).
Because the spec explicitly tells to do so.
Page 75. Note the difference between 11.6.1 steps 5-8 and 11.6.2 steps 5-7.
11.6.1 - describes how addition operator works
1-4. ...
5. Let lprim be ToPrimitive(lval).
6. Let rprim be ToPrimitive(rval).
7. If Type(lprim) is String or Type(rprim) is String, then
7a. Return the String that is the result of concatenating ToString(lprim) followed by ToString(rprim)
8. Return the result of applying the addition operation to ToNumber(lprim) and ToNumber(rprim)
11.6.2 - describes how subtraction operator works
1-4. ...
5. Let lnum be ToNumber(lval).
6. Let rnum be ToNumber(rval).
7. Return the result of applying the subtraction operation to lnum and rnum
Summary
In case of addition if any of the operands when converted to primitive value without any hints suddenly becomes a string the second one is converted to a string too. In case of subtraction both operands are converted to a number.
There is no dedicated string concatenation operator in JavaScript**. The addition operator + performs either string concatenation or addition, depending on the type of operands:
"1" + 1 // "11"
1 + "1" // "11"
1 + 1 // 2
There is no opposite of concatenation (I think) and the subtraction operator - only performs subtraction regardless of the type of operands:
"1" - 1 // 0
1 - "1" // 0
1 - 1 // 0
"a" - 1 // NaN
** The . operator in PHP and & operator in VB are dedicated string concatenation operators.
+ is both an addition operator for numeric variables, and a concatenation operator for strings.
Whenever there's a string after a +, Javascript will choose to use the + as a concatenation operator and convert (typed) as many terms as possible around the string so it can concatenate them. That's just the behaviour of Javascript. (If you tried console.log(23 + 2 + "." + 1 + 5 + "02" + 02);, you'll get the result 25.15022. The number 02 was typed into the string 2 before being concatenated.
- can only be a subtraction operator, so when given a string, it will implicitly change the type of the string "1" into a numeric 1; if it didn't do that, there's no way "1" - 1 would make sense. If you tried console.log(23 + 2 + 1 + 5 - "02" + 03); you'll get 32 - the string 02 gets converted into the number 2. The term after the - must be able to be converted into a number; if you tried console.log(23 - 2 - "." - 1 - 5 - 02 - "02"); you'll get NaN returned.
More importantly, if you tried console.log(23 + 2 + "." + 1 + 5 - "02" + 03);, it will output 26.15, where everything before - was treated as a string (because it contains a string ".", and then the term after the - is treated as a number.
According to the standard EcmaScript 262. The + and - operators behave differently when strings are involved. The first converts every value to a string. The second converts every value to a number.
From the standard:
If Type(lprim) is String or Type(rprim) is String, then Return the
String that is the result of concatenating ToString(lprim) followed by
ToString(rprim)
This rules implies that if in the expression there is a string value, all values involved in the + operation are converted to a string. In JavaScript when the + operator is used with strings, it concatenates them. This is why console.log("5"+1) returns "51". 1 is converted to a string and then, "5" + "1" are concatenated together.
Nevertheless, the above rule doesn't apply for the - operator. When you are using a - all values are converted to numbers according to the Standard (see below). Therefore, in this case, "5" is converted to 5 and then 1 is subtracted.
From the standard:
5 Let lnum be ToNumber(lval).
6 Let rnum be ToNumber(rval).
Operator definition from the standard EcmaScript 262.
Operator + : http://www.ecma-international.org/ecma-262/5.1/#sec-11.6.1
Operator - : http://www.ecma-international.org/ecma-262/5.1/#sec-11.6.2
Using plus and a string "" you basically return a string because you are performing a concatenation:
typeof ("" + 1 + 0) // string
typeof (1 + 0) // number
When using - instead you convert to a number as string concatenation is possible:
typeof ("" - 1 + 0) // number