College Mathematics

Mohave Community College

Kelsey Uhles

May 3, 2014

In math we must know how to classify different numbers. Numbers can be classified into groups which with a little bit of studying are easy to understand over time. Terms in math are thrown around easily and if you don’t understand the terms math will suddenly become much more difficult. The terms and groups that I am referring to are where the different numbers fall into different groups. These groups are Natural numbers, Whole numbers, Integers, Rational numbers, Real numbers, and Irrational numbers.

First Natural numbers which are what we use and see as our counting numbers. These numbers consist of these simple numbers 1, 2, 3, 4… and so on. Whole numbers are the next numbers which include all natural numbers along with the number zero which means that they are for example 0, 1, 2, 3, 4… and so on. Integers can also be whole numbers but also can be whole numbers with a negative sign in front of them. Integers are the individual numbers such as -4, -3, -2, -1, 0, 1, 2, 3, 4… and so on. Rational numbers include integers along with fractions, and decimals. Examples for Rational numbers include ¼, -¾, 7.82, 2, 123/25, 0.3333. Irrational numbers do not include integers or fractions. Although Irrational numbers are the only group that is classified with numbers that can have a decimal value that can continue for however long with no specific pattern unlike rational numbers. An example of an irrational number could be pi. Pi which we usually just round to 3.14 is actually 3.1415926535897932384626433832795… and this continues on for trillions of digits. And last comes Real numbers which include natural numbers, whole numbers, integers, rational number...

... middle of paper ...

...er is rational such as √2 , we can then go to the next step. Recalling that refers only to the positive square root of 2, this means that could be written as the quotient of two positive integers, such as √2 =a/b, where the fractions in lowest terms. We can assume that a and b have no common factors. We can then use simple algebra to find out the conclusion as the following:

√2b=a

(√2b)^2=a^2

2b^2=a^2

With this we are able to determine that a^2 is in fact an even number and that a^2 has 2 as a factor. Since a^2= axa it says that 2 must be a factor of a. Which says that a itself is an even number but that a^2 has 4 as a factor, and therefore 2b^2 has 4 as a factor. Then b^2 has 2 as a factor so that b^2 is an even number. So a/b would not be in its lowest terms since both a and b have 2 as a factor which shows that √2 is an irrational number and cannot be rational.

Mohave Community College

Kelsey Uhles

May 3, 2014

In math we must know how to classify different numbers. Numbers can be classified into groups which with a little bit of studying are easy to understand over time. Terms in math are thrown around easily and if you don’t understand the terms math will suddenly become much more difficult. The terms and groups that I am referring to are where the different numbers fall into different groups. These groups are Natural numbers, Whole numbers, Integers, Rational numbers, Real numbers, and Irrational numbers.

First Natural numbers which are what we use and see as our counting numbers. These numbers consist of these simple numbers 1, 2, 3, 4… and so on. Whole numbers are the next numbers which include all natural numbers along with the number zero which means that they are for example 0, 1, 2, 3, 4… and so on. Integers can also be whole numbers but also can be whole numbers with a negative sign in front of them. Integers are the individual numbers such as -4, -3, -2, -1, 0, 1, 2, 3, 4… and so on. Rational numbers include integers along with fractions, and decimals. Examples for Rational numbers include ¼, -¾, 7.82, 2, 123/25, 0.3333. Irrational numbers do not include integers or fractions. Although Irrational numbers are the only group that is classified with numbers that can have a decimal value that can continue for however long with no specific pattern unlike rational numbers. An example of an irrational number could be pi. Pi which we usually just round to 3.14 is actually 3.1415926535897932384626433832795… and this continues on for trillions of digits. And last comes Real numbers which include natural numbers, whole numbers, integers, rational number...

... middle of paper ...

...er is rational such as √2 , we can then go to the next step. Recalling that refers only to the positive square root of 2, this means that could be written as the quotient of two positive integers, such as √2 =a/b, where the fractions in lowest terms. We can assume that a and b have no common factors. We can then use simple algebra to find out the conclusion as the following:

√2b=a

(√2b)^2=a^2

2b^2=a^2

With this we are able to determine that a^2 is in fact an even number and that a^2 has 2 as a factor. Since a^2= axa it says that 2 must be a factor of a. Which says that a itself is an even number but that a^2 has 4 as a factor, and therefore 2b^2 has 4 as a factor. Then b^2 has 2 as a factor so that b^2 is an even number. So a/b would not be in its lowest terms since both a and b have 2 as a factor which shows that √2 is an irrational number and cannot be rational.

Related

- Better Essays
## What Is Imaginary And Complex Numbers?

- 1196 Words
- 3 Pages

The fourth classification is rational numbers. These are any positive or negative number that can be written as a fraction, including zero, and is commonly known as Q. Not above, but beside rational numbers are irrational numbers. These are numbers that can not be written as a fraction, such as decimals that continue forever, such as pi. The symbol is R/Q, which represents real numbers excluding

- 1196 Words
- 3 Pages

Better Essays - Good Essays
## How can we find a large prime number

- 1336 Words
- 3 Pages
- 4 Works Cited

Prime numbers are numbers that have exactly two divisors. The number one is not included because it only has one divisor, itself. The smallest prime number is two, then three, then five, and so on. This list goes on forever and the largest known primes are called Mersenne primes. A Mersenne prime is written in the form of 2p-1.

- 1336 Words
- 3 Pages
- 4 Works Cited

Good Essays - Satisfactory Essays
## The Phi Function

- 1317 Words
- 3 Pages

My second task is to check that if these are correct: f(7x4) = f(7) x f(4) and f(6x4) = f(6) x f(4) then create some of my own and check that if they are equal to each other or not. Part 1 ====== (1) f(3) = 2 The factors of f(3) are: 1 and 3. The integers, which are less than 3, are 1 and 2. The table below shows the integers, factors and whether it fits into the expression the number of positive integers less than n which have no factor (other than 1) in common (are co-prime) with n. Integers Factors Does it fit into expression? Yes or No 1 1 yes 2 1,2 yes This table shows you that the number of positive integers less than three and has no other common factor other than 1 is two integers: 1 and 2.

- 1317 Words
- 3 Pages

Satisfactory Essays - Good Essays
## Aristolte´s Law of Excluded Middle

- 662 Words
- 2 Pages
- 2 Works Cited

This implies that p also divides their difference P − p1p2 · · · pn = 1A prime number p is an integer greater than one which is only divisible by one and itself ￼ ￼1, which is absurd. This contradicts our assumption that there are no other primes then p1,p2,...,pn. Generally the laws of thought are considered the basis for any thought, discourse or discussion. They cannot be proved or disproved and to deny them is self-contradictory. It is widely known that there are mathematicians who d... ... middle of paper ... ...roperty P, since X is infinite.

- 662 Words
- 2 Pages
- 2 Works Cited

Good Essays - Good Essays
## Integer Constant Essay

- 850 Words
- 2 Pages

There are three types of Integer constants. They are i) Decimal Constant ii) Octal Constant iii) Hexa Decimal Constant Decimal Constant A decimal integer constant is made up of digits 0 to 9 in any combination. The first digit should not be zero. Example for valid decimal integer constants i) 10 ii) 20 iii) 30 The following are invalid decimal integer constants 17,300 - Comma is not allowed 0732 - The

- 850 Words
- 2 Pages

Good Essays - Satisfactory Essays
## Beyond Pythagoras Math Investigation

- 1011 Words
- 3 Pages

32 9 42 16 52 25 62 36 72 49 82 64 92 81 102 100 112 121 As shown in the above table, there are no square numbers with a difference of anywhere near 1. Part 1: Aim: To investigate the family of Pythagorean Triplets where the shortest side (a) is an odd number and all three sides are positive integers. By putting the triplets I am provided with in a table, along with the next four sets, I can search for formulae or patterns connecting the three numbers. Pythagorean Triplet (n) 1st Number (a) 2nd Number (b) 3rd Number (c) Area (cm) Perimeter (cm) 1 2 3 4 5 6 7 3 5 7 9 11 13 15 4 12 24 40

- 1011 Words
- 3 Pages

Satisfactory Essays - Better Essays
## We Cannot Have A Successful Society If Zero Is Not Involved

- 1319 Words
- 3 Pages
- 4 Works Cited

The symbol for zero was two slashes with a blank space between them. Unlike the decimal value system where we have ten distinct symbols to 2 represent zero through nine, the Babylonian’s only had two symbols: a vertical wedge for one and a crescent for ten. Zero in the sexagesimal base system only signified the absence of units of a certain order. The Babylonians did not use zero as “the number zero” as we do today. The concept of twenty minus twenty was still unknown to them.

- 1319 Words
- 3 Pages
- 4 Works Cited

Better Essays - Better Essays
## Binary

- 985 Words
- 2 Pages

Denary Binary 5 ... ... middle of paper ... ...Binary Number System | World of Mathematics Summary, n.d.). This led to Binary being called the machine language because it is very easy to interpret 0 and 1. A machine such as computer can see 0 and 1 as on and off (Leverkuhn, n.d.). For example, a computer processor has inside of it millions of switches that can be turned on and off. This system of on and off tells the computer what it needs to do.

- 985 Words
- 2 Pages

Better Essays - Good Essays
## Number Theory Essay

- 976 Words
- 2 Pages

1. Introduction Mathematics is the language of patterns and relationships, and is used to describe anything that can be quantified. Number theory is one of the largest and oldest branches of mathematics. The main goal of number theory is to discover interesting and unexpected relationships. It is devoted primarily to the study of natural numbers and integers.

- 976 Words
- 2 Pages

Good Essays - Better Essays
## Egyptian Math

- 1038 Words
- 3 Pages
- 5 Works Cited

The first concept was that the Egyptians had a thorough knowledge of the twice-times table. The second concept was that they had the ability to find two-thirds of any number (Gillings 3). This number could be either integral or fractional. The Egyptians used the fraction 2/3 used with sums of unit fractions (1/n) to express all other fractions. Using this system, they were able to solve all problems of arithmetic that involved fractions, as well as some elementary problems in algebra (Berggren).

- 1038 Words
- 3 Pages
- 5 Works Cited

Better Essays