# Tricks With Big Numbers

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Extracting Characters From Keywords Tricks With Big Numbers So Where Are We Now?

Now that we have the string representation of all the digits and the letter `'e'`, we can use JavaScript’s exponent notation to construct strings that represent large numbers such as `10100` and `101000`:

• Form the strings `'1e100'` and `'1e1000'`
• Coercing these strings to numbers gives `1e+100` and `Infinity`
• Coercing these numbers back to strings to give `'1e+100'` and `'Infinity'`
• Extract the characters `'+'`, `'I'` and `'y'`

## Plus Sign

It might seem almost magical that the `'+'` sign can be obtained from a string containing only the characters `1e100`; however, when this string is coerced to a number then back to a string, JavaScript helpfully inserts the `'+'` for us…

``````  +'1e100'          // Create the string and coerce to a number -> 1e+100
(+'1e100')+[]      // Overload plus to convert the number back to a string -> '1e+100'
((+'1e100')+[])[2]  // Extract the character at index 2 -> '+'
``````

Here’s the above code with `'e'`, `1` and `0` represented in their encoded form:

`````` +(+!![]+(!![]+[])[+!![]+!![]+!![]]+(+!![])+(+[])+(+[]))                 // Coerce string '1e100' to number 1e+100
+(+!![]+(!![]+[])[+!![]+!![]+!![]]+(+!![])+(+[])+(+[]))+[]              // Coerce back to string '1e+100'
(+(+!![]+(!![]+[])[+!![]+!![]+!![]]+(+!![])+(+[])+(+[]))+[])[!![]+!![]]  // Extract character at index 2 -> '+'
``````

## Two More Alphabetic Characters

The number `1e+1000` is too large for JavaScript to store as a 64-bit floating point number, so instead, it simply returns the keyword `Infinity`. This is very helpful because it contains the previously unavailable characters `'I'` and `'y'`

`````` +(+!![]+(!![]+[])[+!![]+!![]+!![]]+(+!![])+(+[])+(+[])+(+[]))           // Number Infinity
+(+!![]+(!![]+[])[+!![]+!![]+!![]]+(+!![])+(+[])+(+[])+(+[]))+[]        // Coerce to string 'Infinity'
(+(+!![]+(!![]+[])[+!![]+!![]+!![]]+(+!![])+(+[])+(+[])+(+[]))+[])[+[]]  // Extract character at index 0 -> 'I'
// Extract character at index 7 -> 'y'
(+(+!![]+(!![]+[])[+!![]+!![]+!![]]+(+!![])+(+[])+(+[])+(+[]))+[])[!![]+!![]+!![]+!![]+!![]+!![]+!![]]
``````