Talk:Inequation

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Lead sentence

"In mathematics, an inequation is a statement that two objects or expressions are not the same."

I almost choked, reading that. An equation is a *problem*, which consists in finding the (any, all) value(s) some unknown entity may have if some equality is to be satisfied. Accordingly, an inequation is a problem, which consists in finding the (any, all) value some unknown entity may have if some inequality is to be satisfied. Since "inequalty" is defined elsewhere as "a statement about the relative size or order of two objects", inequations are thingies like x <= a, or x < a, depending.

A. Bossavit, 16 2 06

Do you have a source? Melchoir 00:00, 17 February 2006 (UTC)[reply]

I can see that "4=2+2" is a statement, but I don't see it as a problem to be solved. Only some equations/inequations/inequalities fall into the category of "problems to be solved", while they ALL fall into the category of statements. The distinction between an inequality and an inequation is well established on Wikipedia in several places. Check the Table of mathematical symbols for one such example. capitalist 03:28, 18 February 2006 (UTC)[reply]

An inequality is an inequation. "Problem to be solved" seems like a point of view. For example, someone could claim that i = sqrt(-1) is a problem to be solved, while for many there's no problem to be solved there. Since 1 < 2, then it's true that 2 =/= 3. So every inequality is an inequation, in an ordered field.

Agreed, but the reverse is not true; x=/=y does not imply x < y, so every inequation is not an inequality. The article makes the same distintion between the two. EDIT: Actually though, as the article already points out, x=/=y implies either x>y or x<y (in a linearly ordered set), so in this case an inequation would always be an inequality as well. But in the more general case, isn't it true that an inequation is a statement that the two expressions are not necessarily equal, but could be equal? At any rate, there certainly is a useful distinction to be made between the two terms, which is my main point. capitalist 03:33, 23 February 2006 (UTC)[reply]