Handout 2 - Pre-lims - Mathematics in the Modern World

A complex system of words and symbols, either spoken or written, used by a particular community as a means of communication.

• Language

• Words

• Sentences

• Expression

Statement l: Every language has its vocabulary (the words) and its rules for combining these words into complete thoughts (the sentences).

Statement ll: Math is comprised of primarily two things: numbers and symbols.

• Statement l is true

• Statement ll is true

• Both statements are true

• Both statements are false

Statement l: In English, nouns are used to name things we want to talk about (like people, places, and things); whereas sentences are used to state complete thoughts.

Statement ll: The mathematical analog of a word will be called an expression. Thus, an expression is a name given to a mathematical operation.

• Statement l is true

• Statement ll is true

• Both statements are true

• Both statements are false

Statement l: In English, nouns are used to name things we want to talk about (like people, places, and things); whereas sentences are used to state the ideas of an object.

Statement ll: The mathematical analog of a ‘noun’ will be called an expression. Thus, an expression is a name given to a mathematical object of interest.

• Statement l is true

• Statement ll is true

• Both statements are true

• Both statements are false

Statement l: An expression is the mathematical analog of an English noun; it is a correct arrangement of mathematical symbols used to represent a mathematical object of interest.

Statement ll: An expression does not state a complete thought; it does not make sense to ask if an expression is true or false. The most common expression types are numbers, sets, and functions.

• Statement l is true

• Statement ll is true

• Both statements are true

• Both statements are false

Able to make very fine distinctions

• Precise

• Concise

• Powerful

Able to say things briefly

• Precise

• Concise

• Powerful

A collection of objects, and in mathematical discourse, these objects are mathematical ones such as numbers, points in space.

• Sets

• Functions

• Relations

The members of this are usually called its elements, and the symbol ∈ is usually read “is an element of”.

• Sets

• Functions

• Relations

A relation between a set of inputs having one output each.

• Sets

• Functions

• Relations