What is an integer? { ... -3, -2, -1, 0, 1, 2, 3, ... }
Integers are the whole numbers, negative whole numbers, and zero. For example,
43434235, 28, 2, 0, -28, and -3030 are integers, but numbers like 1/2,
4.00032, 2.5, Pi, and -9.90 are not. We can say that an integer is in the
set: It is often useful to think of the integers as points along a 'number line', like this:
Note that zero is neither positive nor negative.
About integers
The terms even and odd only apply to integers;
Another way to say this is that zero is even since it can be written in the form 2*n, where n is an integer. Odd numbers can be written in the form 2*n + 1. Again, this lets us talk about whether negative numbers are even and odd:
Every positive integer can be factored into the product of prime numbers, and there's only one way to do it for every number. For instance,
Most mathematicians, at least when they're talking to each other, use Z to refer to the set of integers. In German the word "zahlen" means "to count" and "Zahl" means "number." Mathematicians also use the letter N to talk about the set of positive integers, in other words the set From the Dr. Math archives:
Consecutive Integers (High School/Algebra) Introduction to Negative Numbers (Elementary/Subtraction) Is Zero Even, Odd, or Neither? (Elementary/About Numbers) Sets and Integer Pairs (High School/Discrete Math) Sets and Subsets (Middle School/Algebra) Partitioning the Integers (High School/Discrete Math) Why is 1 not considered prime? (Middle School/About Numbers) On the Web
6th Grade Math Class Integer Pictures - Oak Point Intermediate School Rational Numbers 5/1, 1/2, 1.75, -97/3 ...A rational number is any number that can be written as a ratio of two integers (hence the name!). In other words, a number is rational if we can write it as a fraction where the numerator and denominator are both integers.
The term "rational" comes from the word "ratio," because the rational numbers are the ones that can be written in the ratio form p/q where
Every integer is a rational number, since each integer So the set of all rational numbers will contain the numbers 4/5, -8, 1.75 (which is 7/4), -97/3, and so on.
Is .999 repeating a rational number? Well, a number is rational if it can be written as A/B
From the Dr. Math Archives:
About Rational Numbers (Middle School/About Numbers) Is a Ratio Rational or Irrational? (High School/Analysis) On the Web:
Rational Number - Eric Weisstein's World of Mathematics Rational Numbers Real Numbers Complex Numbers Irrational Numbers sqrt(2), pi, e, the Golden Ratio ...Irrational numbers are numbers that can be written as decimals but not as fractions. An irrational number is any real number that is not rational. By real number we mean, loosely, a number that we can conceive of in this world, one with no square roots of negative numbers (such a number is called complex.) A real number is a number that is somewhere on a number line, so any number on a number line that isn't a rational number is irrational. The square root of 2 is an irrational number because it can't be written as a ratio of two integers.
Other irrational numbers include the square root of 3, the square root of 5, pi, e, and the golden ratio. (For more information about pi and e, see Pi is an irrational number because it cannot be expressed as a ratio (fraction) of two integers: it has no exact decimal equivalent, although 3.1415926 is good enough for many applications. The square root of 2 is another irrational number that cannot be written as a fraction. In mathematics, a name can be used with a very precise meaning that may have little to do with the meaning of the English word. ("Irrational" numbers are NOT numbers that can't argue logically!)
From the Dr. Math Archives:
Golden Ratio and Golden Rectangle (Elementary/Golden Rectangle) Irrational Pi (High School/Transcendental Numbers) The Number e (High School/Transcendental Numbers) Meaning of Irrational Exponents (High School/Algebra) Irrational Powers (College/Modern Algebra) Proof that Sqrt(2) is Irrational (High School/Square Roots) Proving the Square Root of 3 Irrational (High School/Square Roots) Are Transcendentals Irrational? (High School/Transcendental Numbers) On the Web:
Irrational Numbers - Jim Loy RJN's More Digits of Irrational Numbers Page More information can be found by searching the Dr. Math archives or the Math Forum site for "integer" or "rational" or "irrational" (just the word, not the quotes). |
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