Ch3Definitions


 * Here are some definitions we will be using in Chapter 3**



__**generalization**__ - a conclusion made about an entire set by testing several members of that set

i__**nductive reasoning**__ - using a series of examples to reach a conclusion

__**counter example**__ - An example which disproves a proposition.

__**conjecture**__ - an educated guess

__**proof**__ - an argument that shows something (like a theorem) is true beyond any doubt.

__**deductive reasoning**__ - observation of an event occurring a number of times and then generalizing that it will happen under the same circumstances all the time


 * __given__** - statement of fact

__**direct proof**__- a way of showing the truth or falsehood of a given statement by a combination of established facts,

__i**ndirect proof**__ - the statement to be proved is assumed to be false and then the contradiction is proven


 * __postulate__** - statement so simple and direct that it is obviously true


 * __axiom__** - like a postulate: statement so simple and direct that it is obviously true

__**theorem**__ - an assertion proved to be true using the rules of logic

__**reflexive property**__ - a quantity or item is equal to itself, a=a


 * __symmetric property__** - if a=b then b=a and ab=ba

__**transitive property**__ - if a=b and b=c then a=c

__**equivalence relation**__ - relation between two members of a set when they are proven reflexive, transitive and symmetric

__**substitution postulate**__ - a quantity may be substituted for its equal in any expression and equation

__**partition postulate**__ - the whole is equal to the sum of its parts

__**addition postulate**__ - If equal quantities are added to equal quantities, the sums are equal.

__**angle addition postulate**__ - if D is inside angle ABC then angle ABD+angle DBC = angle ABC

__**subtraction postulate**__ - If equal quantities are subtracted from equal quantities, the differences are equal.

__**multiplication postulate**__ - If equal quantities are multiplied by equal quantities, the products are equal.

__**division postulate**__ - If equal quantities are divided by equal quantities, the quotients are equal.


 * __powers postulate__** - if a=b, then a2 = b2

__**roots postulate**__ - if a=b and a is not equal to zero then the square root of a = the square root of b.