Basic Mathematics - Real Numbers and Calculus Overview

Vocabulary flashcards covering basic mathematical concepts, types of numbers, order properties of real numbers, and introductory calculus terms from Chapter 0.1.

Veritas

A component of the Universitas Indonesia motto meaning truth.

Probitas

A component of the Universitas Indonesia motto meaning honesty.

Iustitia

A component of the Universitas Indonesia motto meaning justice.

Calculus

The branch of mathematics that studies change.

Differential calculus

The branch of calculus that studies rates of change and involves derivatives, which measure the rate of change of one quantity with respect to another (e.g., velocity, acceleration).

Integral calculus

The branch of calculus that studies accumulation and involves integrals, which measure the accumulation of a quantity (e.g., area, volume, distance).

Digit

A symbol used to represent numbers in mathematics. There are 10 digits in the decimal system ($0, 1, 2, 3, 4, 5, 6, 7, 8, 9$) and 2 in binary ($0, 1$).

Number

A mathematical concept used to quantify something, which can be represented using one or several digits or written/spoken words.

Natural numbers

The set of numbers defined as $\mathbb{N} = \{1, 2, 3, 4, 5, \dots\}$.

Integers

The set of numbers defined as (\mathbb{Z} = {\dots, -3, -2, -1, 0, 1, 2, 3, \dots}), where (\mathbb{Z}) comes from Zahlen, the German word for "number".

Rational numbers

Numbers formed by the ratio (quotient) of 2 integers, defined as $\mathbb{Q} = \left\{\frac{m}{n} : m, n \in \mathbb{Z}, n \neq 0\right\}$, which have repeating decimal representations.

Irrational numbers

Numbers that are not a ratio of 2 integers (denoted as $\bar{\mathbb{Q}}$), such as $\sqrt{2}$, $\sqrt{5}$, $\sqrt[4]{3}$, $\pi$, and $e$, which have non-repeating decimal representations.

Real numbers

The set of numbers $\mathbb{R} = \mathbb{Q} \cup \bar{\mathbb{Q}}$, combining rational and irrational numbers, forming the foundation of Calculus.

Decimal

A representation of a number without using a fraction.

Trichotomy

An order property of real numbers stating that for any real numbers $x$ and $y$, exactly one of $x < y$, $x = y$, or $x > y$ holds.

Transitivity

An order property of real numbers stating that if $x < y$ and $y < z$, then $x < z$.

GeoGebra

An application supporting the learning of Basic Mathematics, available online at www.geogebra.com and as a desktop version called GeoGebra Calculator Suite.