The real numbers were introduced to give x² = -1 a solution.

Practice question · True or false

The real numbers were introduced to give $x^{2} = -1$ a solution.

Hints

Does $x^{2} = -1$ have a real solution?
What did the reals actually fix?

Show the answer

False

Why

False. The reals fill the gaps the rationals leave, $x^{2} = 2$ has no rational solution but does have a real one. $x^{2} = -1$ has no real solution either; that is what forced the complex numbers. Each extension is driven by a specific equation, and getting which equation right is the point.

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The real numbers were introduced to give x2=−1x^{2} = -1x2=−1 a solution.

Practise Number Systems

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The real numbers were introduced to give $x^{2} = -1$ a solution.