sync main

Author: bogdanbacosca

1-js/02-first-steps/05-types/article.md

@@ -68,9 +68,20 @@ We'll see more about working with numbers in the chapter <info:number>.
 
 ## BigInt [#bigint-type]
 
-In JavaScript, the "number" type cannot represent integer values larger than <code>(2<sup>53</sup>-1)</code> (that's `9007199254740991`), or less than <code>-(2<sup>53</sup>-1)</code> for negatives. It's a technical limitation caused by their internal representation.
+In JavaScript, the "number" type cannot safely represent integer values larger than <code>(2<sup>53</sup>-1)</code> (that's `9007199254740991`), or less than <code>-(2<sup>53</sup>-1)</code> for negatives.
 
-For most purposes that's quite enough, but sometimes we need really big numbers, e.g. for cryptography or microsecond-precision timestamps.
+To be really precise, the "number" type can store larger integers (up to <code>1.7976931348623157 * 10<sup>308</sup></code>), but outside of the safe integer range <code>±(2<sup>53</sup>-1)</code> there'll be a precision error, because not all digits fit into the fixed 64-bit storage. So an "approximate" value may be stored.
+
+For example, these two numbers (right above the safe range) are the same:
+
+```js
+console.log(9007199254740991 + 1); // 9007199254740992
+console.log(9007199254740991 + 2); // 9007199254740992
+```
+
+So to say, all odd integers greater than <code>(2<sup>53</sup>-1)</code> can't be stored at all in the "number" type.
+
+For most purposes <code>±(2<sup>53</sup>-1)</code> range is quite enough, but sometimes we need the entire range of really big integers, e.g. for cryptography or microsecond-precision timestamps.
 
 `BigInt` type was recently added to the language to represent integers of arbitrary length.
 
@@ -213,7 +224,7 @@ The `symbol` type is used to create unique identifiers for objects. We have to m
 
 ## The typeof operator [#type-typeof]
 
-The `typeof` operator returns the type of the argument. It's useful when we want to process values of different types differently or just want to do a quick check.
+The `typeof` operator returns the type of the operand. It's useful when we want to process values of different types differently or just want to do a quick check.
 
 A call to `typeof x` returns a string with the type name:
 
@@ -263,14 +274,16 @@ Some people prefer `typeof(x)`, although the `typeof x` syntax is much more comm
 
 There are 8 basic data types in JavaScript.
 
-- `number` for numbers of any kind: integer or floating-point, integers are limited by <code>±(2<sup>53</sup>-1)</code>.
-- `bigint` is for integer numbers of arbitrary length.
-- `string` for strings. A string may have zero or more characters, there's no separate single-character type.
-- `boolean` for `true`/`false`.
-- `null` for unknown values -- a standalone type that has a single value `null`.
-- `undefined` for unassigned values -- a standalone type that has a single value `undefined`.
-- `object` for more complex data structures.
-- `symbol` for unique identifiers.
+- Seven primitive data types:
+    - `number` for numbers of any kind: integer or floating-point, integers are limited by <code>±(2<sup>53</sup>-1)</code>.
+    - `bigint` for integer numbers of arbitrary length.
+    - `string` for strings. A string may have zero or more characters, there's no separate single-character type.
+    - `boolean` for `true`/`false`.
+    - `null` for unknown values -- a standalone type that has a single value `null`.
+    - `undefined` for unassigned values -- a standalone type that has a single value `undefined`.
+    - `symbol` for unique identifiers.
+- And one non-primitive data type:
+    - `object` for more complex data structures.
 
 The `typeof` operator allows us to see which type is stored in a variable.
 

1-js/02-first-steps/08-operators/article.md

@@ -50,8 +50,9 @@ The result of `a % b` is the [remainder](https://en.wikipedia.org/wiki/Remainder
 For instance:
 
 ```js run
-alert( 5 % 2 ); // 1, a remainder of 5 divided by 2
-alert( 8 % 3 ); // 2, a remainder of 8 divided by 3
+alert( 5 % 2 ); // 1, the remainder of 5 divided by 2
+alert( 8 % 3 ); // 2, the remainder of 8 divided by 3
+alert( 8 % 4 ); // 0, the remainder of 8 divided by 4
 ```
 
 ### Exponentiation **
@@ -68,7 +69,7 @@ alert( 2 ** 3 ); // 2³ = 8
 alert( 2 ** 4 ); // 2⁴ = 16
 ```
 
-Just like in maths, the exponentiation operator is defined for non-integer numbers as well. 
+Just like in maths, the exponentiation operator is defined for non-integer numbers as well.
 
 For example, a square root is an exponentiation by ½:
 
@@ -80,7 +81,7 @@ alert( 8 ** (1/3) ); // 2 (power of 1/3 is the same as a cubic root)
 
 ## String concatenation with binary +
 
-Let's meet features of JavaScript operators that are beyond school arithmetics.
+Let's meet the features of JavaScript operators that are beyond school arithmetics.
 
 Usually, the plus operator `+` sums numbers.
 
@@ -194,18 +195,18 @@ Here's an extract from the [precedence table](https://developer.mozilla.org/en-U
 | Precedence | Name | Sign |
 |------------|------|------|
 | ... | ... | ... |
-| 15 | unary plus | `+` |
-| 15 | unary negation | `-` |
-| 14 | exponentiation | `**` |
-| 13 | multiplication | `*` |
-| 13 | division | `/` |
-| 12 | addition | `+` |
-| 12 | subtraction | `-` |
+| 14 | unary plus | `+` |
+| 14 | unary negation | `-` |
+| 13 | exponentiation | `**` |
+| 12 | multiplication | `*` |
+| 12 | division | `/` |
+| 11 | addition | `+` |
+| 11 | subtraction | `-` |
 | ... | ... | ... |
 | 2 | assignment | `=` |
 | ... | ... | ... |
 
-As we can see, the "unary plus" has a priority of `15` which is higher than the `12` of "addition" (binary plus). That's why, in the expression `"+apples + +oranges"`, unary pluses work before the addition.
+As we can see, the "unary plus" has a priority of `14` which is higher than the `11` of "addition" (binary plus). That's why, in the expression `"+apples + +oranges"`, unary pluses work before the addition.
 
 ## Assignment
 
@@ -303,9 +304,9 @@ Such operators have the same precedence as a normal assignment, so they run afte
 ```js run
 let n = 2;
 
-n *= 3 + 5;
+n *= 3 + 5; // right part evaluated first, same as n *= 8
 
-alert( n ); // 16  (right part evaluated first, same as n *= 8)
+alert( n ); // 16
 ```
 
 ## Increment/decrement
@@ -437,7 +438,7 @@ The list of operators:
 - RIGHT SHIFT ( `>>` )
 - ZERO-FILL RIGHT SHIFT ( `>>>` )
 
-These operators are used very rarely, when we need to fiddle with numbers on the very lowest (bitwise) level. We won't need these operators any time soon, as web development has little use of them, but in some special areas, such as cryptography, they are useful. You can read the [Bitwise Operators](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Expressions_and_Operators#Bitwise) chapter on MDN when a need arises.
+These operators are used very rarely, when we need to fiddle with numbers on the very lowest (bitwise) level. We won't need these operators any time soon, as web development has little use of them, but in some special areas, such as cryptography, they are useful. You can read the [Bitwise Operators](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Expressions_and_Operators#bitwise_operators) chapter on MDN when a need arises.
 
 ## Comma