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Why can't we provide size of array in Javascript?

Why can't we provide size of array in JavaScript?
I mean even if it is possible why don't we why we just simply define the array.

Because standard arrays in JavaScript aren't really arrays at all (spec | post on my blog), they're just objects backed by Array.prototype with special handling for a class of property names ("array indexes"), a special length property, and a built-in literal notation. They aren't contiguous blocks of memory as in some other languages (barring optimization, of course).
I have a question in my mind about why can't we provide size of array in JavaScript ??
You can create an array with a given length via Array(n) where n is the length as a number. But again, it doesn't preallocate memory for that many slots or anything. You just end up with a sparse array with length set to n and no entries in it:
var a = Array(42);
console.log(a.length); // 42
console.log(0 in a); // false, it doesn't have an entry 0
a.forEach(function(entry) { // Never calls the callback
console.log(entry); // because the array is empty
});
I mean even if it is possible why don't we why we just simply define the array.
Because it serves no purpose.
Now, for typed arrays (Uint8Array and similar), we do indeed create them with a specific length (var a = new Uint8Array(42);), and that length is fixed (cannot change), because they're true arrays.

You can provide size of array. If its not given, you can add multiple values dynamically.
var arr = new Array(5);

You can provide size of array in java-script.
Java-script array is different from array in C language.
You can read more on following link
understanding-javascript-arrays

You can provide a size of an array and that size of an array will not change in the program.
Array is an object backed by Array.prototype, so there is a function called seal.
var myArray = Object.seal([5, 6, "saurabh", "text"]); // this is an array of size 4 fixed.
//myArray.push('new text'); //throw exception error
console.log(myArray[2]); //"saurabh"
myArray[0] = "change text";
console.log("print myArray: ", myArray);
You can read more over here:
https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Object/seal

Javascript create 2d Array with ids as array key

I need an array structure that includes the user id as array key and can store more information about that user (2 dimensional array). In my case if he is allowed to perform database requests, these are represented by request id and true/false.
Each user can have multiple requests
For example:
User id =14 and requests ids =22 and true and 45 and false
User id =12 and requests ids =44 and false and 77 and false
It should look like this:
var users_rights={14:{22:true,45:false},12:{44:false,77:false}}
I’m struggling with js syntax since
var id[14] ;
Creates an array with 14 elements and the rest of the array is empty but I want an array where at the 14 position all my requests information are stored.

You can use the [] syntax with regular JS objects like the one you describe. Simple example:
var ob = {10: {11:true}, 12: {13: false}};
console.log(ob[10]); //Displays the object {11:true}
console.log(ob[10][11]); //Displays true

If you create the array first, then assign the values you will edit only the nth element e.g.
var id = [];
id[14] = 'xyz'
Gives an array with 14 undefined's and 'xyz' as the 15th element.

It sounds as though you don't want an array at all, you want an object with object values for its properties (or if you're using ES2015, a Map of Maps).
Your
var users_rights={14:{22:true,45:false},12:{44:false,77:false}}
(which is perfectly valid syntax, other than you should have a ; at the end) gives you the former: You index into it with the user ID (14) and then index into the object you get as a result with the request IDs (22 and/or 45), which gives you a boolean value.
You create an object like this:
var users_rights = {};
You add a property to it for the key 14 like this:
users_rights[14] = {};
You add properties to that the same way:
users_rights[14][22] = true;
users_rights[14][45] = false;
These objects are just plain objects, not arrays. Brackets notation works with them just fine (in fact, it's the fact that brackets notation works with objects that makes it work with arrays, because standard arrays in JavaScript aren't really arrays at all).

javascript array indexing with large integers

I have a strange problem. I need a multidimensional javascript array that has numeric indexes e.g.:
MyArray = new Array();
$(".list-ui-wrapper").each(function(){
var unique = $(this).attr('id').replace(/[^\d.]/g,'');
MyArray ["'"+unique+"'"] = new Array();
});
The unique is a 8 digit integer. So if I dont wrap it inside the quotes, the ListUI_col_orders array will become extremly big, because if the unique = 85481726 then javascript will fill the array with 85481725 undefined elements before the the new empty array at the 85481726th index.
My problem is that later if i generate the unique again i cannot access the array anymore:
var unique = $(this).attr('id').replace(/[^\d.]/g,'');
console.log(MyArray [unique]); // undefined
console.log(MyArray ['"'+unique+'"']); // undefined
console.log(MyArray [unique.toString()]); // undefined
Any tips?

If you are going to use an array that's mostly sparse, then use a Hash table instead.
eg, set your variable as follows:
ListUI_col_Orders = {};
Then your indexing will be a key, so you don't have to worry about all the interstitial elements taking up space.

...because if the unique = 85481726 then javascript will fill the array with 85481725 undefined elements before the the new empty array at the 85481726th index.
No, it won't. JavaScript standard arrays are sparse. Setting an element at index 85481725 results in an array with one entry, and a length value of 85481726. That's all it does. More: A myth of arrays
The problem is that you're trying to retrieve the information with a different key than the key you used to store it. When storing, you're using a key with single quotes in it (actually in the key), on this line of code:
MyArray ["'"+unique+"'"] = new Array();
Say unique is 85481726. That line then is equivalent to this:
MyArray ["'85481726'"] = new Array();
Note that the key you're using (the text between the double quotes) has ' at the beginning and end. The actual property name has those quotes in it. Since it doesn't fit the definition of an array index, it doesn't affect length. It's a non-index object property. (How can you add a property to an array that isn't an array index? Arrays are not really arrays, see the link above.)
Later, you never use that key when trying to retrieve the value:
var unique = $(this).attr('id').replace(/[^\d.]/g,'');
console.log(MyArray [unique]); // undefined
console.log(MyArray ['"'+unique+'"']); // undefined
console.log(MyArray [unique.toString()]); // undefined
The keys you tried there were 85481726, "85481726" (with double quotes), and 85481726 again. Note that you never tried '85481726' (with single quotes), which is the key you used originally. Since you didn't use the same key, you didn't get the value.
Either use consistent quotes, or (much better) don't use quotes at all. Don't worry about the array length being a large number, JavaScript arrays are inherently sparse. Adding an entry with a large index does not create several thousand undefined entries in front of it.
All of that being said, unless you need the "array-ness" of arrays, you can just use an object instead. Arrays are useful if you use their features; if you're not using their array features, just use an object.
More about the sparseness of arrays: Consider this code:
var a = [];
a[9] = "testing";
console.log(a.length); // 10
Although the length property is 10, the array has only one entry in it, at index 9. This is not just sophistry, it's the actual, technical truth. You can tell using in or hasOwnProperty:
console.log(a.hasOwnProperty(3)); // false
console.log("3" in a); // false
When you try to retrieve an array element that doesn't exist, the result of that retrieval is undefined. But that doesn't mean there's an element there; there isn't. Just that trying to retrieve an element that doesn't exist returns undefined. You get the same thing if you try to retrieve any other property the object doesn't have:
var a = [];
a[9] = "testing";
console.log(a[0]); // undefined
console.log(a[200]); // undefined
console.log(a["foo"]); // undefined
Final note: All of this is true of the standard arrays created with [] or new Array(). In the next spec, JavaScript is gaining true arrays, created with constructors like Int32Array and such. Those are real arrays. (Many engines already have them.)

Memory assignment to arrays

I was wondering if any one knows how memory is handled with JS arrays if you have an array that starts with a high value.
For example, if you have:
array[5000] = 1;
As the first value in the array, everything before 5000 simply does not exist, will the amount of memory assigned to the array cater for the unassigned 4999 positions prior to it... or will it only assign memory to the value in the array for [5000] ?
I'm trying to cut down on the amount of memory used for my script so this led to me wondering about this question :)

When assigning a value to the 5000th key, not the whole array is populated:
var array = []; // Create array
array[5000] = 1;
'1' in array; // false: The key does not exists
Object.keys(array); // 5000 (it's the only key)
If you want to blow your new browser with arrays, populate a typed array:
var array = new ArrayBuffer(6e9); // 6 Gigs
Both can be verified easily in Chrome: Open the console and memory console (Shift+Esc), and paste the code. window.a=new Array(6e9); or window.a=[];window[6e9]=1; doesn't result in a significant memory increase,
while window.a=new ArrayBuffer(6e9); crashes the page.
PS. 6e9 === 6000000000

Javascript is really interpreted and run by the browser, so it depends on how the browser implements this behavior. In theory, once you do array[5000], you have an array of 5001 elements, all except the 5001st being undefined.
Though if I were the one implementing the logic for running such script, undefined would be the default value if not assigned to anything else, meaning I could probably get away with defining a map with 1 entry assigning key 5000 to value 1. Any accesses to any other value in the array would automatically return undefined, without having to do unnecessary work.
Here's a test of this here. As you can see, the alert is seen immediately.

JS arrays are actually not arrays as you know them from other programming languages like C, C++, etc. They are instead objects with a array like way of accessing them. This means that when you define array[5000] = 1; You actually define the 5000 property of the array object.
If you had used a string as the array key you would have been able to access the index as a property as well to demonstrate this behavior, but since variable names can't start with a number array.5000 would be invalid.
array['key'] = 1;
alert( array.key ); // Gives you 1
This means that arrays will probably be implemented much like objects, although each implementation is free to optimize, thus giving you the behavior you except from objects where you can define object.a and object.z without defining the whole alphabet.

Creating multi-dimensional arrays in javascript, error in custom function

I was trying to define an array (including other arrays as values) in a single javascript statement, that I can loop through to validate a form on submission.
The function I wrote to (try to) create inline arrays follows:
function arr(){
var inc;
var tempa = new Array(Math.round(arguments.length/2));
for(inc=0; inc<arguments.length; inc=inc+2) {
tempa[arguments[inc]]=arguments[inc+1];
}
return tempa;
}
This is called three times here to assign an array:
window.validArr = arr(
'f-county',arr('maxlen',10, 'minlen',1),
'f-postcode',arr('maxlen',8, 'minlen',6)
);
However in the javascript debugger the variable is empty, and the arr() function is not returning anything. Does anyone know why my expectations on what this code should do are incorrect?
(I have worked out how to create the array without this function, but I'm curious why this code doesn't work (I thought I understood javascript better than this).)

Well from what your code does, you're not really making arrays. In JavaScript, the thing that makes arrays special is the management of the numerically indexed properties. Otherwise they're just objects, so they can have other properties too, but if you're not using arrays as arrays you might as well just use objects:
function arr(){
var inc;
var tempa = {};
for(inc=0; inc<arguments.length; inc=inc+2) {
tempa[arguments[inc]]=arguments[inc+1];
}
return tempa;
}
What you're seeing from the debugger is the result of it attempting to show you your array as a real array should be shown: that is, its numerically indexed properties. If you call your "arr()" function as is and then look at (from your example) the "f-county" property of the result, you'll see something there.
Also, if you do find yourself wanting a real array, there's absolutely no point in initializing them to a particular size. Just create a new array with []:
var tempa = [];

Your code works. Just inspect your variable, and you will see that the array has the custom keys on it. If not expanded, your debugger shows you just the (numerical) indixed values in short syntax - none for you.
But, you may need to understand the difference between Arrays and Objects. An Object is just key-value-pairs (you could call it a "map"), and its prototype. An Array is a special type of object. It has special prototype methods, a length functionality and a different approach: to store index-value-pairs (even though indexes are still keys). So, you shouldn't use an Array as an associative array.
Therefore, their literal syntax differs:
var array = ["indexed with key 0", "indexed with key 1", ...];
var object = {"custom":"keyed as 'custom'", "another":"string", ...};
// but you still can add keys to array objects:
array.custom = "keyed as 'custom'";