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Multiplicative Identity

Rule

Multiplicative Identity

The multiplicative identity, also called the identity element, is the element of a group that multiplied by every other element leaves each element unchanged. For example, for real numbers that element is 1.1. 71=72.361=2.36341=34π1=π\begin{aligned} 7\cdot1&=7 &\qquad\qquad 2.36 \cdot1 &= 2.36 \\[1em] \frac{3}{4}\cdot1&=\frac{3}{4} &\qquad\qquad \pi \cdot1&=\pi \end{aligned} The exception is 00 since 01=0.0\cdot1=0. Therefore, it's excluded when talking about the identity of real numbers.