Deductions
- complex number has part quaternion ⇐ (imaginary unit is a quaternion), (complex number has part imaginary unit)
- negative real number has part quaternion ⇐ (imaginary unit is a quaternion), (negative real number has part imaginary unit)
- complex unit has part quaternion ⇐ (imaginary unit is a quaternion), (complex unit has part imaginary unit)
- quaternion is for example -i ⇐ (-i is a quaternion), (is a is inverse of is for example)
- quaternion is for example imaginary unit ⇐ (imaginary unit is a quaternion), (is a is inverse of is for example)
- imaginary unit is a quaternion ⇐ (complex number is subclass of quaternion), (imaginary unit is a complex number)
- -i is a quaternion ⇐ (complex number is subclass of quaternion), (-i is a complex number)
- 0 number class is subclass of quaternion ⇐ (nonzero real number is subclass of quaternion), (nonzero real number is opposite of 0 number class)
- negative real number is subclass of quaternion ⇐ (non-negative real number is subclass of quaternion), (non-negative real number is opposite of negative real number)
- quaternion is for example −3 ⇐ (−3 is a quaternion), (is a is inverse of is for example)
- quaternion is for example 3 ⇐ (3 is a quaternion), (is a is inverse of is for example)
- 3 is a quaternion ⇐ (real number is subclass of quaternion), (3 is a real number)
- −3 is a quaternion ⇐ (real number is subclass of quaternion), (−3 is a real number)
- non-negative real number is subclass of quaternion ⇐ (non-negative real number is subclass of nonzero real number), (nonzero real number is subclass of quaternion), (is subclass of is a transitive relation)
- nonzero real number is subclass of quaternion ⇐ (nonzero real number is subclass of real number), (real number is subclass of quaternion), (is subclass of is a transitive relation)
- real number is subclass of quaternion ⇐ (complex number is subclass of quaternion), (complex number is opposite of real number)