What is a real number, a whole number, an integer, a rational number, and an irrational number?

Question

What is a real number, a whole number, an integer, a rational number, and an irrational number?

Answer 1

all #s

#s like 4, -1, 7... not 4.7, 2.47823, or -23.48, or 5 1/7

3.25, 4.25, 5.5... (ends or like "1/3" so .3s go on forever not 5.287904629081694529714... (no repeat..)

opposite of the one above

Answer 2

real numbers are like our counting numbers

( 1,2,3,4,5) , whole numbers begin with o              ( 0,1,2,3,4) integers include number that are negative (-2,-1,0, 1,2,3), ration numbers are fractions and whole Numbers for example a fraction looks like this 2/3, a whole number is also a rational number because it can be written over 1, "5/1". it counts,so rational number s              ( 1/2,2/3, .9/2, 2, 3), irrational numbers are like numbers such as pie~ 3.14, root 3/2, those are irrational. as far as what these number are, they're just numbers, they count for something, they mean something in life because they can be used in every day life so that's what they are, they're useful and they're real, that's that! :)

Answer 3

a whole # is any # starting from 0 all the way to infinity.

and integer is simply any #.

a rational number is a number that has an end, or an actual value. for example 321.0025698 is rational ecause if someone asked you you could tell them the entire number.

and irrational number has no end. for example pie 3.14213465464.... is irrational because it never ends.

im not sure what a real number is.

google it.

Answer 4

A real number is a number which not imaginary

A whole number is a number which is not broken

A integer is a something that integrates...

A rational number is a number that is reasonable

An irrational number is a number that irritates you... :D

Well don't be irritated, in algebra,

A real number is any number (actually there are such an imaginary number, and complex number, these numbers are excluded!). It can be a whole number, an integer, a fraction, a decimal number, a rational number or an irrational number.

A whole number is any number which is not a fraction or a decimal number, examples are 1, 2, 7, 89. It is always an integer (traditionally it refers only to positive, however there is an ambiguity if it includes the negative)  and a rational number.

An integer is any number which can be either positive and negative but not a fractional number. It is also a whole number. Examples are -1,256, -589, -1, 0, 1, 569, 5,236. It is always a rational number.

A rational number is any number (either an integer or a fraction) which is can classified into three groups:

*non-repeating and terminating* -  can be an integer like 17, -253 or a fraction like 1/2 which is equal to 0.5, 1/4=0.25 (Hence, terminating - it ends)

*repeating and terminating* - examples are 111.111, 233.3333, 0.555

*repeating and non-terminating - examples are 12.121212121212......, 7/9 which is equal to 0.777777777777777.......

Remember an integer is always an rational number, but a rational number is not always an integer.

An irrational number is a number that is non-repeating and non-terminating, a number which cannot be expressed in exact fraction, and most well known examples are the pi and square root of 2.

See: http://en.wikipedia.org/wiki/Irrational_...

Hope it helps... :D

Answer 5

A whole number is a quantity that directly expresses the size of a finite set of discrete objects. Ie., if we have the set A = {a, b, c} or a set B consisting of a rock, some other rock, and yet another rock, both A and B are sets whose quantity or size is defined to be represented by the whole number 3. Adding a single object or removing a single object from a set gives the set a different size/quantity/whole number.

An integer is more general, in that it allows us to do basic algebra by including numbers that, when added to a whole number, is the same as decreasing that whole number. In particular, each whole number W is an integer and is associated with another integer -W such that when these two integers are added, we get 0.

The set of rational numbers is even more general and allows us to do algebra with multiplication and division. Whereas before, we could multiply two numbers a and b as a copies of b or b copies of a, we now have numbers such that multiplying b with the new number 1/b gives us 1. We also allow the multiplication of 1/b with any element, so we can get numbers like a/b, where a and b have no common divisors. This introduces the concept of numbers as ratios and allows us to talk about portions of discrete objects that are not so easy to think about in terms of collections of discrete objects (ie., lengths, liquids, continuous materials, etc.).

The set of real numbers "completes" the set of rational numbers by defining r to be a real number if given a set of rational numbers (finite or infinite) that is bounded from above (there is some rational number greater than all the numbers in this set) then r is the least number greater than all the numbers in the set or equal to the greatest number in the set. Note that this concept of there being a smallest number greater than all the members of a set is missing from rational numbers. For example, the set {1/2} gives us the real number 1/2, while the infinite set containing all numbers of the form Sum_{i=0}^n ((-1)^i)/(2i - 1) for all whole numbers n gives us the real number pi/4. This adds certain "missing numbers" that are convenient to have around, such as sqrt(2), pi, and so on. The real numbers give us the idealism of continuity in geometry. Whether the "real" numbers have anything to do with reality is a matter for philosophy, as we can only ever measure a finite amount of digits with finite amount of error in reality.

An irrational number is simply a real number that is not a rational number, like sqrt(2) or pi/4.