Prove: Irrational Numbers Have Rational Numbers Between

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The discussion centers on proving that there exists at least one rational number between any two irrational numbers. Participants argue against this claim by referencing the irrational numbers √2 and √2, asserting that no rational number exists between them. The conversation highlights the need for a proof method, with suggestions including analysis and topology, but ultimately concludes that the assertion is false in the specific case of identical irrational numbers.

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sedaw
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need to prove that : between any two irrational numbers there is at least one rational number .

TNX .
 
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It's not true, there is none between [itex]\sqrt{2}[/itex] and [itex]\sqrt{2}[/itex].

Also, what would you like to use for a proof? Analysis? Topology?
 
CompuChip said:
It's not true, there is none between [itex]\sqrt{2}[/itex] and [itex]\sqrt{2}[/itex].

Also, what would you like to use for a proof? Analysis? Topology?


Analysis, for x and y that x<y
 

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