Title: Mathematical Language and Symbols
Author: Prof. Liwayway Memije-Cruz
Language facilitates communication and clarifies meaning.
It allows individuals to express themselves and maintain their identity.
The language of mathematics is designed to express mathematicians' thoughts clearly and succinctly:
Precise: Makes very fine distinctions.
Concise: Communicates ideas briefly.
Powerful: Accurately conveys complex thoughts.
Examples include mathematical representations like k=0, mc², and A = r².
In English, nouns name entities (people, places, things), while sentences express complete thoughts.
Example: "Anne hates mathematics."
Nouns: "Anne, mathematics"; Verb: "hates."
Mathematical analogue of a noun is an expression: names a mathematical object.
The analogue of a sentence in mathematics is a sentence, which, like English, must convey a complete thought.
English vs. Mathematics:
Noun (English) corresponds to Expression (Mathematics):
Examples: Carol, Idaho, book vs. 5, 2+3, 1/2.
Sentence (English) corresponds to Sentence (Mathematics):
Examples: "The capital of Idaho is Boise." vs. "3+4=7."
Various expressions can represent the same number:
Examples: 5, 2+3, -10 ÷ 2, (6-2)+1, 1 + 1 + 1 + 1 + 1.
Generate synonyms for "similarity."
Provide various expressions for the number three:
Standard name: Three.
Plus sign: 1+2.
Minus sign: 5-2.
Division sign: 6÷2.
Sentences can be classified as true or false; truth is fundamental in mathematical language.
Exercises include identifying verbs and determining the truth value of sentences about the capital of Idaho and mathematical statements.
Fill in sentences with relevant nouns, verbs, or mathematical expressions and highlight verbs.
Sentences covering various operations:
t + 3
T + 3 = 3 + t
This sentence is false.
X + 0 = x
1.x = x
Hat sat bat.
Overview of mathematical symbols.
List of symbols with meanings:
Equals sign: Indicates equality (e.g., 5 = 2 + 3).
Not equal sign: Expresses inequality (e.g., 5 ≠ 4).
Greater than: e.g., 5 > 4.
Less than: e.g., 4 < 5.
Inequality symbols for greater than or equal to, and less than or equal to.
Overview of notations used in set theory:
{}: Encloses elements in a set.
| : Indicates membership in a set.
Proper subset, superset, and cardinality symbols.
Useful resources for further study:
http://www.onemathematicalcat.org
https://www.dpmms.cam.ac.uk/~wtg10/grammar.pdf
https://byjus.com/maths/math-symbols/