MMW 2

Conventions

In language may include:

- subject-verb agreement

- capitalization

- proper usage of punctuation marks

- indentions and margins of a block-type letter

Conventions

In Mathematics, conventions teach us to be careful on what we are dealing with.

Confirmation

It is better than mere assumption.

0-9

10 basic digits

Quantities, Rankings, Denominations, Time

10 basic digits represents?

+ − × ÷

4 fundamental operations

MDAS/PEMDAS

We should always follow:

Robert Recorde in 1557

= → equality sign

Thomas Harriot in 1631

< and > → strict inequalities

Pierre Bouguer in 1734

≤ and ≥ → less than or equal to

Rene Descartes in 1637

x² → exponents in modern notation

Christoff Rudolff in 1525

√ → radical symbol

Albert Girard in 1629

n√ → index within the opening of the radical sign

Christian Kramp in 1808

n! → factorial notation

±

William Oughtred in 1631

± → used in its modern form

Rene Descartes

x, y, z → unknowns

use of x, y, z to represent unknowns is due to

William Jones in 1706

π → pi

Euler in 1727

e → pie (golden ratio)

John Wallis in 1655

∞ → infinity symbol

Johannes Widmann in 1489

+ and −

William Oughtred (St. Andrew's Cross) in 1618

× → Multiplication

Gottfried Wilhelm Leibniz in 1698

• → symbol for multiplication

Johann Rahn in 1659

÷ → division

POWERFUL

It can describe very complex concepts and phenomenon using simple equations and denotations.

PRECISE

It only conveys one and only one thought.

PRECISE

It is less prone to misunderstanding.

Example:

In English:

"You are beautiful" / "Are you beautiful?"

In Mathematics:

3 + 2 = 5

CONCISE

It uses fewer symbols to convey a long narrative sentence.

CONCISE

Long paragraphs of explanation can be organized and compacted into a single number sentence.

Mathematical Symbols

It holds a particular meaning, depending on usage.

Robert Recorde

=

Thomas Harriot

< and >

Rene Descartes

x², x, y, z

Christoff Rudolff

√

Christian Kramp

n!

William Jones

π

Euler

e

John Wallis

∞

Johannes Widmann

+ and −

William Oughtred

×, ±