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Glossary of terms

I

  • Title

    Identities

  • Description

    Not to be confused with an Identity, identities are statements which are true for all values (the mathematical symbol for for all is $\forall)$.

    An identity is identified using a special equals sign with three lines, as below.

  • Example of use

    \[2(x+1) \equiv 2x+2\]
  • See also

  • Title

    Identity

  • Description

    An identity is term from group theory describing an operation which does not change the value of the number being operated upon.

  • Example of use

    Under addition, the identity is $0$ because any number $n + 0 = n$.

    Under multiplication, the identity is $1$ because any number $n \times 1 = n$.

  • See also

  • Title

    iff

  • Description

    iff means If and only if. Just a bit stronger than an ordinary if.

  • Example of use

    A set of numbers have a product of $0$, iff one or more of the set of numbers is $0$.

  • See also

  • Title

    Imaginary numbers

  • Description

    Imaginary numbers ($\mathbb{C}$) are numbers based around multiples of $i$, where $i=\sqrt{-1}$.

  • Example of use

    \[\sqrt{-9} = \sqrt{9} \times \sqrt{-1} = 3i\]

    In this calculation, $3i$ is an imaginary number.

  • See also

  • Title

    Integers ($\Bbb{Z}$)

  • Description

    Integers are all of the counting numbers ($\Bbb{N} = \Bbb{Z}^+$) as well as the negative whole numbers ($\Bbb{Z}$-) and zero ($0$). So any whole number on the real number line, positive or negative or zero, is an integer.

  • Example of use

    $\{-4, -3, -2, -1, 0, 1, 2, 3, 4\} \in \Bbb{Z}$
  • See also

  • Title

    Irrational numbers

  • Description

    An irrational number is one which cannot be written as a fraction (integer $\div$ integer).

  • Example of use

    $\sqrt{2}$ is irrational.

    $\pi$ is irrational

  • See also