Question

Theorem: there is no smallest positive rational number.theorem: there is no smallest positive rational number. a proof by contradiction of the theorem starts by assuming which fact?

Answer 1

Assume there is a smallest rational integer that has the following form: a/b

Then observe that we can define a/(b+1), which is strictly less than a/b because its divisor is bigger and is rational because it is the product of two numbers. Due to the contradiction created by our original claims that a/b is the smallest rational number that is possible, we might conclude that there is no such thing as the smallest rational number.

There can therefore be no smallest rational number because we may always define a smaller rational number than the one we now possess.

What is Rational number ?

Any number that can be expressed as a ratio is considered reasonable. It is therefore possible to represent it as a fraction when the numerator and denominator are both full numbers.

Learn more about Rational number here:

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