simplifying a chain of inequalities - LGG?

Stream: new members

[rzeta0]

Consider the following inequalities

$$\begin{align} a \geq b \\ b = c \\ c > d \end{align}$$

We can't simplify this chain of inequalities down to $a \geq d$. The correct simplification is $a > d$.

Question: Is the logical process of simplifying a chain of inequality called taking the least general generalisation?

That phrase LGG is from symbolic AI (inductive logic programming). Is there a different phrase used in pure mathematics?

[Ted Hwa]

I don't think there's a name for it in pure mathematics. Also, $a \ge d$ would not be wrong, just not the best result possible.

[rzeta0]

Hi Ted - I've edited to fix the mathematical error. Hopefully now we can say $a \geq d$ is wrong, and $a > d$ is correct.

Although both versions of question pose a challenge to what I think LGG is !

[Ted Hwa]

Still the same. If $a > d$ is correct, then $a \ge d$ must also be correct, since $a > d$ implies $a \ge d$.

[rzeta0]

H Ted - I think I'll delete this thread, my brain is making terrible errors!