Mathematical Language and Symbols

🧮 Mathematics in Our World

Mathematical Language and Symbols

🗣 What Is Language?

Language

• A complex system of words and symbols

• Can be spoken or written

• Used by a community to communicate ideas

👉 Just like English or Filipino, math also has:

• Vocabulary

• Rules

• Meaning

This part is important kasi ito ‘yung foundation ng topic.

🔢 Language of Mathematics

Math is mainly made up of:

• Numbers

• Symbols

Just like words + grammar = sentences,
numbers + symbols = mathematical statements

✏ Common Mathematical Symbols

👉 In short: Symbols help math say a lot with very little writing.

⭐ Characteristics of Mathematical Language

Math language is:

1. Precise

   • Very exact, walang paligoy-ligoy

2. Concise

   • Short but meaningful

3. Powerful

   • Can express complex ideas easily

🧠 Mnemonic:
PCP → Precise, Concise, Powerful

🔁 English Language vs Mathematical Language

Math works like English, may equivalents lang.

🧩 Expressions

Expression

• Mathematical version ng noun

• Names a mathematical object

• Does NOT state a complete thought

• Cannot be true or false

Examples:

• 5

• 2 + 3

• (6 − 2) + 1

👉 Kahit iba-iba itsura, puwedeng same value.

📌 Important:
You cannot ask if an expression is true or false.

✅ Mathematical Sentences

Mathematical Sentence

• States a complete thought

• Has a verb (usually symbols like =, <, >)

• Can be:

  • Always true

  • Always false

  • Sometimes true / sometimes false

Examples:

• 1 + 2 = 3 → true

• 1 + 2 = 4 → false

• x = 2 → sometimes true

• x + 3 = 3 + x → always true

🧠 Memory tip:
Expression = name
Sentence = statement

🔗 Sets, Functions, and Relations

🧺 Sets

Set

• A collection of mathematical objects

• Elements = members of a set

Symbol:

• ∈ → “is an element of”

Example:

• 5 ∈ P (5 belongs to the set of prime numbers)

👉 Here, “is” does NOT mean equals — it means belongs to.

🔄 Functions

Function

• A mathematical transformation

• Takes an input and produces an output

Examples:

• Square root of n

• Two times n

• Cosine of n

• Logarithm of n

👉 Functions change objects into other objects.

🔗 Relations

Relation

• Describes a relationship between objects

• Behaves like:

  • equals (=)

  • less than (<)

  • element of (∈)

Example:

• 5 < 10

• 3 = 3

👉 Relations help compare things.

🧠 Elementary Logic

Logic connects statements.

❌ Negation

Negation

• Opposite of a statement

• Symbol: ~

Example:

• “Today is Monday”

• Negation: “Today is not Monday”

➕ Conjunction

Conjunction

• Uses and

• Symbol: ∧

Example:

• p: Mariella eats fries

• q: Mae drinks soda

• p ∧ q: Mariella eats fries and Mae drinks soda

➗ Disjunction

Disjunction

• Uses or

• Symbol: ∨

Example:

• p ∨ q: The clock is slow or the time is correct

➡ Implication

Implication

• “If p, then q”

• Symbol: ⇒

Parts:

• p = premise

• q = conclusion

Example:

• If Helen finishes homework, then she cleans her room.

👉 If p is true, q must be true.

📌 QUICK RECAP (Exam Saver)

• Math is a language

• Expressions = names

• Sentences = complete thoughts

• Sets = collections

• Functions = transformations

• Relations = comparisons

• Logic = connects statements

🧠 FINAL MEMORY TRICKS

• Expression = NO truth value

• Sentence = TRUE or FALSE

• ∈ = belongs to

• Function = input → output

• ∧ = and

• ∨ = or

• ⇒ = if–then