give me the definitons of these words:linear inequality

intersection of two sets
union of two sets
undefined
quantity of interest
term
unit
constraint
nonviable
solve
viable

1 answer

Here are the definitions for the words/phrases you requested:

  1. Linear Inequality: A mathematical expression that represents a relationship between two linear expressions using an inequality sign (such as <, >, ≤, or ≥). For example, \(2x + 3 < 7\) is a linear inequality.

  2. Intersection of Two Sets: The set containing all elements that are common to both sets. If set A = {1, 2, 3} and set B = {2, 3, 4}, then the intersection A ∩ B = {2, 3}.

  3. Union of Two Sets: The set containing all elements that are in either one set or the other or in both. If set A = {1, 2, 3} and set B = {2, 3, 4}, then the union A ∪ B = {1, 2, 3, 4}.

  4. Undefined: A term used to describe a situation where a value or concept does not have a clear or valid meaning. In mathematics, it often refers to expressions that do not result in a real or meaningful number, such as division by zero.

  5. Quantity of Interest: A specific value or measure that is being analyzed or evaluated within a problem or experiment, often serving as the primary focus of study or calculation.

  6. Term: In mathematics, a term is a single mathematical expression that can be a number, a variable, or a product of numbers and variables (e.g., \(3x\) or \(4\)). In context, it can also refer to individual components of an expression or sequence.

  7. Unit: A standard quantity used to measure and express physical quantities, such as length, mass, time, etc. Examples include meters for length, kilograms for mass, and seconds for time.

  8. Constraint: A condition or limitation that restricts the possible values of variables in a mathematical problem or system. In optimization problems, constraints define the feasible region for solutions.

  9. Nonviable: Referring to an option, solution, or course of action that is not feasible, practical, or acceptable. In a biological context, it can also refer to cells or organisms that are incapable of growth or reproduction.

  10. Solve: To find the answer to, or the value of, a mathematical problem or equation. Often this involves isolating a variable or finding solutions that satisfy given conditions.

  11. Viable: Pertaining to a solution, option, or course of action that is feasible, practical, and capable of working effectively. In biological terms, it can refer to cells or organisms that can survive, develop, and reproduce.

If you need further explanations or context for any of these terms, feel free to ask!