Define the following terms with respect to the domain calculus: domain variable, range relation, atom, formula, and expression.

Short Answer

Expert verified
A domain variable is a quantity within a specified domain. Range relation describes the output values produced by a function or relation. An atom is an expression or proposition that cannot be divided into smaller parts. A formula is a mathematical rule expressed as an equation. An expression in calculus is a combination of variables, constants, and operations that represents a certain quantity.

Step by step solution

01

Define domain variable

A domain variable is a quantity that can take on one or more values within a specified or implied domain. In calculus, it could be the set of all possible input values (usually x) for which a function or relation is defined.
02

Explain range relation

A range relation describes the set of all output values (usually y) produced by a function or relation for the specified or implied domain. In other words, it's the result we get after applying the function to the domain. It's important to note that not all elements in a range must have a corresponding element in the domain.
03

Define atom

In the context of calculus and mathematical logic, an atom is an expression or proposition that cannot be divided into smaller or simpler components. Atoms are the simplest units of a formula and are used to build more complex expressions or formulas.
04

Explain the term formula

A formula is an equation that expresses a relationship or rule mathematically. In calculus, a formula can describe transformations from the domain to the range, general properties of functions or sequences, or other quantitative relationships. Formulas are often made up of mathematical symbols, numbers, and variables.
05

Define expression

An expression in calculus is a combination of variables, constants, and operations (like addition, subtraction, multiplication, or division) that represents a particular quantity. Expressions do not contain equality or inequality symbols—those are reserved for equations and inequalities, respectively.

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