What is the exact meaning of these similar words in math: property , axiom , postulate , theorem ,rule , law ,principl. What are the differences between them.

Question

What is the exact meaning of these words in math : property , axiom , postulate , theorem , rule , law , principle .

What are the differences between them? 

Tanks in advance!

Answer 1

 

 

 

              An axiom is a proposition regarded as self-evidently true without proof. 

 

 

 

             Postulate is a true statement, which does not require to be proved.

More About Postulate
Postulate is used to derive the other logical statements to solve a problem.
Postulates are also called as axiom.

 

 

A result that has been proved to be true (using facts that were already known).

Example: The "Pythagoras Theorem" proved that for a right angled triangle a2 + b2 = c2

 

Functions are usually represented by a function rule where you express the dependent variable, y, in terms of the independent variable, x. A pair of an input value and its corresponding output value is called an ordered pair and can be written as (a, b).

 

 

-2down vote
A theorem is a statement proved by a chain of reasoning. The theorem is not self evident. It is derived after considering the results of several logical statements (often including other theorems). A famous example of this is the Pythagorean Theorem, which has nearly 400 proofs.

Laws are statements which are inferred by observation. Laws are not proved. Laws are demonstrated based on repeated observations. It expresses a causal relationship between entities under certain conditions, and is often expressed mathematically. The Laws of Thermodynamics (so often quoted without the mathematical context and misstated for that very reason) are good examples.

A theory is an established and respected explanation of a natural phenomenon, acquired through confirmation of its principles through the scientific method - testing, confirmation, and observation and experimentation.

A fact is a true statement under the set conditions. A thing that is indisputably the case. Facts can generally be reproduced to be verified. A single counter example will immediately demote a fact to a false claim.

A proof in science a successful demonstration of a hypothesis under study using evidence and analysis. It is a misconception in many ways, since science actually can't prove anything for certain. In this sense, "proof" is a simplified way of saying "greatly enhanced confidence".

A rule is an informal axiom that expresses a philosophical point. A rule governs how a subject behaves under certain circumstances. A rule indicates increased chance of a certain outcome when a subject is in a certain state. Newton's "rules" or Occam's Razor are examples.

A Conjecture is a statement not (yet) proven, but which intuitively seems to be true, or for which the author has some more complex reasons to believes to be likely to be true. Some deceivingly simple of those resist centuries of attacks by brightest mathematicians.
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answered May 12 '15 at 3:08

 

 

principal

Principal is the amount of money borrowed or invested

 

In math, properties demonstrate general rules that are used in calculations. The most commonly used properties in day-to-day math are the properties of addition and multiplication. The commutative property of addition, for example, states that no matter how you order the numbers when adding, the result is the same.

 

 

 

 

 

 

      Answers are from Google on the internet...

 

 

                Hope this helps !

                        Oscar

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer 2

In many subjects, we "compare & contrast" different things, such as films, plays, political philosophy, religion.

 

In mathematics, this is relatively unimportant--what is vital is the precise definitions of the terms that we use, and using them correctly. Concentrate on the definitions, given in good textbooks, not 'differences between them!'

Answer 3

Mark is right -- with questions about specific definitions, students should be able to look in their textbook. If you have this question for homework or as preparation for a test, you are likely to find the answer in the body of the math text, and I would guess for something like this, the most recent chapter. You may find information (such as "differences between them") not given in a glossary. You might also have to do a bit of thinking of your own, comparing their similarities to help see how they are different.