# $$\dfrac{1}{0}$$ is a new number?

Algebra Level 3

Recall that we defined $$\sqrt{-1}$$ as a new number to come up with a solution to the equation $x^2+1=0.$

The resulting number system, namely the Complex Number System, preserves the rules of arithmetic$$^1$$ that works for the Real Number System.

Similarly, can't we define $$\dfrac{1}{0}$$ as a new number and thus come up with a number system that includes solution to $$0 \cdot x =1$$ and preserves the rules of arithmetic for the Real Number System?

Footnote:

1. Commutative, Distributive and Associative Laws.
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