# Lightning Talk Outline

## Slide 1 - Infinity
 * Definition
 * Things comes in different sizes
 * Infinity is no different

## Slide 2 - Bijection
 * You can't test infinity by counting
 * If two sets can be paired, they’re the same size
 * If all the chairs in the room are taken, and no one is standing, I know there are exactly as many chairs as their are people

## Slide 3 - Natural Numbers
 * Natural numbers (counting numbers) represent the smallest kind of infinity
 * Unexpected behavior: all even numbers || all odd numbers == all natural numbers
 * Kick out all the odd numbers, and each even number is paired with 2x itself

## Slide 4 - Integers/Rational Numbers
 * A set of integers or rational numbers will share the same behavior

## Slide 5 - Real Numbers
 * Real numbers aren't countable
 * There is no way to line up the reals/naturals so that we are assigning exactly one real number to each natural number
 * Rational numbers are like the stars, irrational numbers are like the blackness

## Slide 6 - Transcendentals
 * Once you have one infinity, you can always make a larger one by creating a set of all subsets of that infinity

## Slide 7 - Achieving Infinity in Ruby
 * `(1 / 0)         #=> ZeroDivisionError: divided by 0`
 * `(1.0 / 0)       #=> Infinity`
 * `Infinity        #=> NameError: uninitialized constant Infinity`
 * `Float::INFINITY #=> Infinity`
 * `(-1.0 / 0)      #=> -Infinity`

## Slide 8 - Properties of Infinity in Ruby
 * `(Infinity == -Infinity) #=> false`
 * `(Infinity >  -Infinity) #=> true`

 * `Infinity + 10 #=> Infinity`
 * `Infinity / 10 #=> Infinity`
 * `Infinity - 10 #=> Infinity`
 * `Infinity * 10 #=> Infinity`

 * `10**10000         #=> really big number`
 * `10**10000 + 0.01  #=> Infinity`

## Slide 8 - NaN
 * `Infinity - Infinity #=> NaN`
 * `Infinity * Infinity #=> NaN`

## Slide 9 - Use Cases
 * Full range of values as expressed by IEEE: `-Infinity < x < Infinity` includes all real numbers
 * Implementing lazy lists: `(200..Float::INFINITY).step(100).take(N)`
 * Examples

## Slide 10 - Infinity and Beyond
 * Toy Story 4 is in theatres now