At least I wasn't alone

]]>Witch1's question was "if x is greater than y then the reciprocal of x is less than y"

Which leads one to think about 3>2 therefore 1/3<2, but I gave the counter-example of 1>0 leads to 1/1>0 (then, having typed, my fingers moved on ...)

]]>What do you call it? Inequality algebra? What do I search on to learn more about rules and techniques?]]>

Let x be greater than y:

x > y

So if we divide both sides by xy:

x/xy > y/xy => 1/y > 1/x

But that statement is only true if xy is positive. Thus, either x is negative or y is negative, but not both, fits as a counter example.

]]>Secondly, if I want to call something irrational in the English sense of the word, then I will.]]>

And yes John, I'm fairly certain that number is irrational.

]]>5.1121231234123451234561234567123456781234567891243456789012345678901123456789012123456789012312345678901234123456789012345 etc... I think it is but I haven't checked the definition lately.]]>

1 and 0

]]>