Axiom
/ˈæk.si.əm/
nounC1
Definition
An axiom is a simple, clear idea or rule that people accept as true right away. It does not need to be proven because it is the starting point for other ideas or reasoning, especially in subjects like mathematics and logic.
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See It in Action
A basic statement accepted as true without proof in math or logic
- •The axiom that parallel lines never meet is important in geometry.
- •Many mathematical systems start by defining some axioms.
- •Without axioms, we cannot build logical arguments.
A general truth or principle accepted by people
- •It is an axiom that hard work leads to success.
- •The idea that honesty is the best policy is often treated as an axiom.
- •In business, the axiom "time is money" guides many decisions.
Make It Stick
- ✓Think of "axiom" like "fact," but one that we accept without proof because it helps us build other ideas.
- ✓Picture a foundation stone in a building—an axiom is like that stone for knowledge; everything else is built on it.
- ✓It feels like a rule everyone agrees on, like "2 + 2 = 4," which we don’t question.
- ✓Sounds like "AXE-ee-um" → imagine an axe cutting through confusion to reveal a clear, simple truth.
- ✓In stories or puzzles, axioms are like the basic rules of the game that players must follow.
- ✓NOT like "theory" (which needs proof and can change), an axiom is accepted as true from the start.
- ✓NOT like "guess" or "opinion," which are uncertain or personal—axioms are certain and shared.
- ✓NOT like "law" (which is a rule made by people or governments)—axioms are basic truths, not created rules.
Try Other Words
- •Principle: a basic truth or rule (Use when talking about general rules in life or science)
- •Postulate: a statement assumed true without proof, especially in math (Use when referring to formal assumptions in math or science)
- •Rule: a guideline to follow (Use in less formal or everyday contexts)
Unboxing
- •Word parts: none clearly separable; "axiom" is a whole word
- •Etymology: From Greek "axiōma," meaning "that which is thought worthy or fit," or "a self-evident truth"
- •Historical development: Used since ancient Greek philosophy and mathematics as a starting truth
- •Modern usage: Commonly used in math, logic, and philosophy to mean a foundational statement accepted without proof
- •Interesting fact: Axioms are the base for building entire systems of knowledge, like how math is built on simple accepted truths
Reflect & Connect
•Can something be an axiom in one culture but not in another? How does that affect knowledge?
•How do axioms help us understand complex ideas by starting with simple truths?
Fill in the blanks
1.In geometry, an axiom is a statement accepted as true ___ needing any proof.
2.People use axioms as the ___ for building more complicated ideas or arguments.
3.Unlike a theory, an axiom does not require ___ before it is accepted.
4.The axiom "time is money" is often used to show the ___ value of time.
5.Axioms are different from opinions because they are generally ___ by everyone.
6.When solving math problems, you start with axioms and then ___ new results.
7.If a statement can be proven false, it cannot be an ___ because axioms must always be true.