Basic identities

Chapter 4 - Algebra Reference

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Additive Identity

a + 0 = a

Multiplicative Identity

1a = a

Multiplicative Inverse

$$\frac{a}{1} = a$$

or

$$\frac{a}{a} = 1$$

Zero Properties of Multiplication

0a = 0

$$\frac{0}{a} = 0$$

Division by Zero

$$\frac{a}{0} = undifined$$

Notes for Division by zero

  • While division by zero is popularly thought to be equal to infinity, this is not technically true. 
  • In some practical applications it may be helpful to think the result of such a fraction approaching positive infinity as a positive denominator approaches zero (imagine calculating current I=E/R in a circuit with resistance approaching zero—current would approach infinity), but the actual fraction of anything divided by zero is undefined in the scope of either real or complex numbers.