What is the name of this inequality?

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In summary, inequalities are mathematical statements that compare two quantities using symbols such as <, >, ≤, or ≥. There are several types of inequalities, including linear, quadratic, absolute value, and rational. To solve an inequality, the variable must be isolated and algebraic operations can be used. Inequalities differ from equations in that they show a relationship between quantities that are not necessarily equal. In science, inequalities are important for describing and analyzing real-life situations, making predictions, and decision-making processes.
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Leo Liu
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Homework Statement
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Relevant Equations
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My prof. calls it the triangle inequality. However the wikipedia page with the same this name shows a special case of it, which is ##|x+y|\leq|x|+|y|##, and my prof. calls it the triangle inequality 2. I wonder what the formal name of the inequality in the picture above is. Thanks in adv.
 
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[tex]|(x-z)+(z-y)| \le |x-z|+|z-y|[/tex]
 
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Leo Liu said:
Homework Statement:: .
Relevant Equations:: .

View attachment 288370
My prof. calls it the triangle inequality. However the wikipedia page with the same this name shows a special case of it, which is ##|x+y|\leq|x|+|y|##, and my prof. calls it the triangle inequality 2. I wonder what the formal name of the inequality in the picture above is. Thanks in adv.
Triangle inequality is correct. The reason why is in post #2 by @anuttarasammyak .
 
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FAQ: What is the name of this inequality?

1. What is an inequality?

An inequality is a mathematical statement that compares two quantities or expressions using symbols such as <, >, ≤, or ≥. It indicates that one quantity is larger or smaller than the other.

2. How is an inequality different from an equation?

An inequality uses symbols to show a relationship between two quantities, while an equation uses an equal sign to show that two expressions are equal. Inequalities also have a range of possible solutions, while equations have only one solution.

3. What are the different types of inequalities?

The three main types of inequalities are linear, quadratic, and exponential. Linear inequalities involve linear expressions, quadratic inequalities involve quadratic expressions, and exponential inequalities involve exponential expressions.

4. How do you solve an inequality?

To solve an inequality, you need to isolate the variable on one side of the inequality symbol and simplify the other side. The solution is the range of values that make the inequality true. However, if you multiply or divide both sides by a negative number, you need to flip the inequality symbol.

5. Why are inequalities important in science?

Inequalities are important in science because they allow us to represent real-world situations where there is a range of possible solutions. They are used to model relationships between variables in various scientific fields, such as physics, chemistry, and biology.

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