A fact is a statement that can be verified. It can be proven to be true or false through objective evidence. An opinion is a statement that expresses a feeling, an attitude, a value judgment, or a belief. It is a statement that is neither true nor false.
Q. Which is an example of an statement that is accepted without proof?
Parallel Postulate
Table of Contents
- Q. Which is an example of an statement that is accepted without proof?
- Q. What statement are said to be true without any proof?
- Q. Can a mathematical statement be true before it has been proven?
- Q. What statement requires proof before it is accepted as a true statement?
- Q. What does it mean for something to be mathematically true?
- Q. How important are the patterns we see everyday?
- Q. What do we call the mathematical statement assumed to be true?
- Q. What is an example of an axiom?
Q. What statement are said to be true without any proof?
Geometry Chapter 2-Part 1
| A | B |
|---|---|
| Postulate | A statement that describes a fundamental relationship between the basic terms of geometry-Postulates are accepted as true without proof. |
| Theorem | A statement or conjecture that can be proven true by undefined terms, definitions, and postulates |
Q. Can a mathematical statement be true before it has been proven?
If a statement is true for some interpretation (model) and false for some other, then it is independent of the theory and undecidable within the theory. But the fact, that a statement is undecidable within a theory, cannot be proven within the theory itself.
Q. What statement requires proof before it is accepted as a true statement?
If the initial statement is agreed to be true, the final statement in the proof sequence establishes the truth of the theorem. Each proof begins with one or more axioms, which are statements that are accepted as facts.
Q. What does it mean for something to be mathematically true?
lo.logic. As I understand it, mathematics is concerned with correct deductions using postulates and rules of inference. From what I have seen, statements are called true if they are correct deductions and false if they are incorrect deductions.
Q. How important are the patterns we see everyday?
The ability to recognize and create patterns help us make predictions based on our observations; this is an important skill in math. Understanding patterns help prepare children for learning complex number concepts and mathematical operations. Patterns allow us to see relationships and develop generalizations.
Q. What do we call the mathematical statement assumed to be true?
Axiom. The word ‘Axiom’ is derived from the Greek word ‘Axioma’ meaning ‘true without needing a proof’. A mathematical statement which we assume to be true without a proof is called an axiom.
Q. What is an example of an axiom?
In mathematics or logic, an axiom is an unprovable rule or first principle accepted as true because it is self-evident or particularly useful. “Nothing can both be and not be at the same time and in the same respect” is an example of an axiom.
