Final answer:
Inequality symbols like ≠, <, >, and ≤ are used in mathematics to express that two values are not equal or to compare their sizes. They are important for writing mathematical and statistical expressions as well as for comparing quantities in various scientific contexts.
Step-by-step explanation:
The question deals with inequality symbols used in mathematics to compare two expressions or values. Such symbols include ≠ (not equal to), < (less than), > (greater than), and ≤ (less than or equal to). When writing mathematical statements or hypotheses, it is important to use the correct symbols to convey the intended meaning accurately. For example, the alternative hypothesis in statistical tests is often denoted with H or H₁ and uses symbols like ≠, >, or <, but never an equals sign. Comparing areas or magnitudes also relies on the use of inequalities, such as A₁ > A₂ to indicate that area A₁ is greater than area A₂.
Here are a few examples demonstrating the use of inequality symbols:
- When comparing metric measurements, we may say that 5 kilograms is greater than 4 kilograms: 5 kg > 4 kg.
- In a hypothesis test, if we expect a sample mean to be different from a known population mean, we might write H₁: µ ≠ µ₀.
- Considering approximate values in mathematics, we might state that π is approximately equal to 3.14, using the symbol ≈: π ≈ 3.14.
- When comparing forces in physics, if force A is larger than force B, we would write A > B.