Class: Math::SetTheory::EmptySet

Inherits:

NumberSet

• Object
• Closure
• NumberSet
• Math::SetTheory::EmptySet

Includes:

Singleton

Defined in:

lib/ruuuby/math/set_theory/discrete/empty_set.rb

Overview

aliased by+∅+

Instance Attribute Summary

Attributes inherited from NumberSet

#name, #symbol, #𝔠

Attributes inherited from Closure

#axioms

Instance Method Summary

• #initialize ⇒ EmptySet constructor

  A new instance of EmptySet.

• #∋?(n) ⇒ Boolean
• #⊂?(s) ⇒ Boolean

  False (always).

• #⊃?(s) ⇒ Boolean
• #⊆?(s) ⇒ Boolean

  True (always).

• #⊇?(s) ⇒ Boolean

  True (always).

Methods inherited from NumberSet

#countable?, #countably_infinite?, #finite?, #uncountable?, #∌?, #⊄?, #⊅?

Constructor Details

#initialize ⇒ EmptySet

Returns a new instance of EmptySet.

# File 'lib/ruuuby/math/set_theory/discrete/empty_set.rb', line 13

def initialize; super(:∅, 0); end

Instance Method Details

#∋?(n) ⇒ Boolean

Parameters:

• n (*)

Returns:

• (Boolean)

# File 'lib/ruuuby/math/set_theory/discrete/empty_set.rb', line 18

def ∋?(n); false; end

#⊂?(s) ⇒ Boolean

Returns false (always).

Parameters:

• s (*)

Returns:

• (Boolean) —

  false (always)

# File 'lib/ruuuby/math/set_theory/discrete/empty_set.rb', line 23

def ⊂?(s); false; end

#⊃?(s) ⇒ Boolean

Parameters:

• n (*)

Returns:

• (Boolean)

# File 'lib/ruuuby/math/set_theory/discrete/empty_set.rb', line 33

def ⊃?(s); false; end

#⊆?(s) ⇒ Boolean

Returns true (always).

Parameters:

• s (*)

Returns:

• (Boolean) —

  true (always)

# File 'lib/ruuuby/math/set_theory/discrete/empty_set.rb', line 28

def ⊆?(s); s.symbol == self.symbol; end

#⊇?(s) ⇒ Boolean

Returns true (always).

Parameters:

• s (*)

Returns:

• (Boolean) —

  true (always)

# File 'lib/ruuuby/math/set_theory/discrete/empty_set.rb', line 38

def ⊇?(s); s.symbol == self.symbol; end