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Page 1: Title and Author

• Title: Mathematical Language and Symbols

• Author: Prof. Liwayway Memije-Cruz

Page 2: Importance of Language

• Language facilitates communication and clarifies meaning.

• It allows individuals to express themselves and maintain their identity.

Page 3: Characteristics of the Language of Mathematics

• 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.

Page 4: English Language Structure

• In English, nouns name entities (people, places, things), while sentences express complete thoughts.

  • Example: "Anne hates mathematics."

  • Nouns: "Anne, mathematics"; Verb: "hates."

Page 5: Mathematics Structure

• 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.

Page 6: Comparing English and Mathematics

• 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."

Page 7: Multiple Representations of Numbers

• Various expressions can represent the same number:

  • Examples: 5, 2+3, -10 ÷ 2, (6-2)+1, 1 + 1 + 1 + 1 + 1.

Page 8: Exercises

1. Generate synonyms for "similarity."

2. Provide various expressions for the number three:

• Standard name: Three.

• Plus sign: 1+2.

• Minus sign: 5-2.

• Division sign: 6÷2.

Page 9: Truth in Mathematical Language

• 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.

Page 10: Fill in the Blanks

• Fill in sentences with relevant nouns, verbs, or mathematical expressions and highlight verbs.

Page 11: Examples of Mathematical Sentences

• Sentences covering various operations:

  • 11. t + 3

  • 12. T + 3 = 3 + t

  • 13. This sentence is false.

  • 14. X + 0 = x

  • 15. 1.x = x

  • 16. Hat sat bat.

Page 12: Mathematical Symbols

• Overview of mathematical symbols.

Page 13: Common 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.

Page 14: Set Theory Notations

• Overview of notations used in set theory:

  • {}: Encloses elements in a set.

  • | : Indicates membership in a set.

  • Proper subset, superset, and cardinality symbols.

Page 15: References

• Useful resources for further study:

  • http://www.onemathematicalcat.org

  • https://www.dpmms.cam.ac.uk/~wtg10/grammar.pdf

  • https://byjus.com/maths/math-symbols/