# What is the difference between axiom and property in algebra?

properties are based on axioms

### Describe the role of axiom systems in algebra?

An axiom in algebra is the stepping stone to solving equations. In order to solve and equation you know how to use the commutative, associative, distributive, transitive and equalilty axiom to solve the basic steps. For example: if you want an equation in the form y = mx + b, given 6x - 3y = 9 you must subtract 6x from both sides giving: -3y = 9-6x. Then you divide by -3 to get y…

### What is the difference between a conjecture and an axiom?

First off, I'll explain what axioms are since they are of fundamental importance to abstract algebra and math in general. In mathematical logic, an axiom is an underivable, unprovable statement that is accepted to be truth. Axioms are, therefore, statements which form the mathematical basis from which all other theorems can be derived. The most well-known modern examples of mathematical axioms are those of the axiomatic set theory known as ZFC. The Zermelo-Fraenkel set theory…

### What is the difference between the zero property of multiplication and the identity property of addition?

Usually, the identity of addition property is defined to be an axiom (which only specifies the existence of zero, not uniqueness), and the zero property of multiplication is a consequence of existence of zero, existence of an additive inverse, distributivity of multiplication over addition and associativity of addition. Proof of 0 * a = 0: 0 * a = (0 + 0) * a [additive identity] 0 * a = 0 * a + 0…

### What is the property allows you to divide the same quantity from both sides of an equality?

It's not so amazing that you can divide both sides by the same quantity. What IS special is the fact that after you do that, the two sides are still equal. And it also works for addition, subtraction, and multiplication. Right there in a nutshell is the whole story of working with equations and solving them. It all rests on the axiom from Algebra that says ... If equals are (added to)/(subtracted from)/(multiplied by)/(divided by)…

### C program to check given two numbers are amicable or not?

Take the numbers, factor them, then make a list of all the proper divisors and add them up. To factor use a Computer Algebra System like Maple, Mathematica or Axiom, if you like. http://en.wikipedia.org/wiki/Amicable_number http://en.wikipedia.org/wiki/Divisor http://axiom-wiki.newsynthesis.org/uploads/chapter-9.13-26.xhtml#sec-9.22

### What does axiom mean?

An axiom is a basic mathematical truth used in proofs, outlined initially by Euclid. Axioms are self-evident and do not need to be proven, they can be combined and used logically to prove more complex mathematical concepts, especially in geometry. Example: "The shortest distance between two points is a straight line."

### What does axiom means?

An axiom is an assumption that is assumed to be true in some mathematical system. The axioms of geometry are historically called postulates. Intuitively an axiom is a statement whose truth is self-evident. Mathematical axioms need not be self-evident or true in any real-world sense. An axiom of one mathematical system may be false in a different system.