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Ask HN:Transitivity property of real numbers

3 points by pencil ↗ HN
Hello HN,

The transitivity property of real numbers says if a>b,b>c then a>c.but when i test this property with real numbers it give's me false results.let a=1,b=2 and c=3 then the transitivity property says if 1>2,2>3 then 1>3 which doesn't make any sense.i'll be glad if someone could comeout with a nice explanation.

5 comments

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wingi
You can only infer something from something true.
btilly
Start with two false assumptions, draw a false conclusion. Where is the problem?
pencil
ya you may be right...let me do some research on real numbers and it's properties and then get back to you!!!!
Kliment
Well, it's very simple. The "if" is the key to it. IF 1 were greater than 2 AND 2 were greater then 3, THEN 1 would be greater than three. Since neither 1>2 nor 2>3 is true, 1>3 is not required to be true by the transitivity property. If I am taller than you and you are taller than your mother, then I am taller than your mother. If either of the assumptions is broken, the conclusion does not hold.
pencil
ah.that's a wise explanation .i even realised that it's just a fundamental law and not a theorem.anyways you made it clear.