How does "+var === +var" work internally to verify if var is numeric?

Seeing this question: Is there a (built-in) way in JavaScript to check if a string is a valid number? and this: jsperf, one of the presented approaches is this (mutatis mutandis):

var a = "123"
var b = "123b"

if ( +a === +a ) // true

if ( +b === +b ) // false

How does this logic work internally in JavaScript to make this possible?

My question is not how to check if a string is a valid number – this is already answered here: Validate decimal numbers in JavaScript - IsNumeric(). I want to understand how the statement +a === +a works.

+ converts the value to a number.

a gets converted to 123 and 123 === 123.

b gets converted to NaN but NaN !== NaN (because NaN is never equal to another NaN according step 4a of the equality rules).

The + operator here is known as the Unary Plus.

The unary plus operator precedes its operand and evaluates to its operand but attempts to converts it into a number, if it isn't already.

+"123" evaulates as 123.

+a === +a
-> +"123" === +"123"
  -> 123 === 123
    -> true

+"123b" evaluates as NaN (Not a Number), as the b character cannot be converted with the Unary Plus as without any prefix (like 0x for hexadecimal) the Unary Plus will assume the value is decimal (0-9). NaN is a special case in that it does not compare against anything, including itself:

NaN === NaN
-> false

NaN !== NaN
-> true

Because of this, our +b test case fails:

+b === +b
-> +"123b" === +"123b"
  -> NaN === NaN
    -> false

If you want both to evaluate to true we can add an isNaN() call at the end:

if ( +a === +a || isNaN(+a) )

if ( +b === +b || isNaN(+b) )

+"123b" is NaN. NaN is not equal to anything, including NaN.