What, if anything, is necessarily true inequalities called?

In summary, inequalities are mathematical expressions that compare two values or quantities using symbols such as <, >, ≤, and ≥. An inequality is necessarily true when it holds for all possible values of the variables involved. Inequalities are different from equations in that they compare values and have a range of solutions, while equations show that two values are equal and have a single solution. An inequality cannot be both true and false, but it may be true for some values of the variables and false for others. Some examples of necessarily true inequalities include <i>x</i> + 5 > <i>x</i>, 2<sup>3</sup> > 2<sup>2</sup>, and <i>x</i
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arildno
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An equality that is true for all members of a specified set is generally called an "identity" (for example x+x=2x is, say, an identity wrt the set of real numbers).

But do inequalities that are true for all members of a specified set have an established name?
(An inequality of that kind would be [itex]x^{2}+1\geq{0}[/itex] for real x).
 
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Yes, identinequalities;;;perhaps not found in English bibliography
 

Related to What, if anything, is necessarily true inequalities called?

1. What are inequalities?

Inequalities are mathematical expressions that compare two values or quantities. They use symbols such as <, >, ≤, and ≥ to indicate the relationship between the two values.

2. What makes an inequality necessarily true?

An inequality is necessarily true when it is true for all possible values of the variables involved. This means that no matter what values are substituted for the variables, the inequality will always hold.

3. How are inequalities different from equations?

Inequalities and equations are both mathematical expressions, but they serve different purposes. Inequalities compare two values, while equations show that two values are equal. Inequalities also have a range of possible solutions, while equations have a single solution.

4. Can an inequality be both true and false?

No, an inequality cannot be both true and false. It can only be one or the other. However, if an inequality contains variables, it may be true for some values of the variables and false for others.

5. What are some examples of necessarily true inequalities?

Some examples of necessarily true inequalities include x + 5 > x, 23 > 22, and x + 3 ≥ x. These inequalities are true for all possible values of x.

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