Intro to Whole Numbers and Number Sets (1.1)

Vocabulary flashcards covering key terms from the lecture on sets, number systems, and whole numbers.

Set

A group of items or objects considered as a single collection, usually written with braces { } and denoted with a capital S.

Natural numbers

The counting numbers: 1, 2, 3, …; an infinite set that starts at 1.

Whole numbers

Natural numbers plus zero (0); the set {0, 1, 2, 3, …}.

Integers

All whole numbers and their negatives (…, -2, -1, 0, 1, 2, …); includes zero but no fractions or decimals.

Fractions

Numbers written as a/b where a and b are integers and b ≠ 0.

Decimals

Numbers written with a decimal point; can be terminating or repeating decimals.

Rational numbers

Numbers that can be written as a/b with integers a and b (b ≠ 0); includes integers and terminating or repeating decimals.

Irrational numbers

Decimals that do not terminate or repeat and cannot be written as a fraction (e.g., π, √2).

Real numbers

The set that combines rational and irrational numbers; all numbers on the number line.

Pi

An irrational number representing the ratio of a circle's circumference to its diameter.

Square root of 2

An irrational number that cannot be expressed as a fraction.

Expanded notation

Writing a number as a sum of digits times their place-value powers of 10 (place-value expansion).

Hindu-Arabic base-10 system

Base-10 numeral system using digits 0–9 with place value (ones, tens, hundreds, etc.).

Place value (ones, tens, hundreds)

The value of a digit depends on its position: 10^0 (ones), 10^1 (tens), 10^2 (hundreds), etc.

Thousands grouping

Grouping digits in sets of three (thousands, millions, billions) to name large numbers.

Number line

A straight line used to graph numbers and visualize their order and distance.

Less than

Symbolized as <; if a < b, a lies to the left of b on the number line.

Greater than

Symbolized as >; if a > b, a lies to the right of b on the number line.

Rounding

Approximating a number to a specified place value using the rounding digit; if the rounding (test) digit is ≥5, round up; otherwise round down.

Writing numbers in words (grouping)

Say numbers by groups of three digits (ones, thousands, millions); example: 3,071,000 = 'three million seventy-one thousand'.