Question

is 5/1 an integer??

Answer 1

yes

Answer 2

if you simplify it, then you'll find that it's an integer (a whole number)

Answer 3

how come? that it is an integer.. 5/1 is a fraction right?

Answer 4

it's both

Answer 5

Yeah.... all integers are fractions (rational numbers) But not all rational numbers are integers :)

Answer 6

but we defined integers as set of numbers that can be written without a fractional or decimal component right? how come that all integers are fractions??

Answer 7

all integers are fractions because 4 is actually 4/1 (<---fraction)

Answer 8

An integer is a number that CAN BE WRITTEN WITHOUT A FRACTIONAL OR DECIMAL COMPONENT

It doesn't say anywhere in the definition that an integer CANNOT BE WRITTEN *WITH* A FRACTIONAL OR DECIMAL COMPONENT.

Rhetoric plays a big role in definitions in Math :P

Answer 9

@zugzwang .. im confused ..

Answer 10

In fact, any number can be written as a non-terminating decimal, if you so wish...

Answer 11

Any real number, that is...

Okay... let's begin with the very beginning: The natural numbers... you know what they are?

Answer 12

yeah, counting numbers..

Answer 13

picture time!

Answer 14

Though that doesn't really help in convincing you that 5/1 is an integer... hang on.
5/1 = 5
correct, @meyjoux ?

Answer 15

yes

Answer 16

5 is an integer, correct?

Answer 17

yes

Answer 18

I prefer the term 'reboot'
:P

Now, @meyjoux
Would it make sense if
5/1 = 5
but 5 is an integer and 5/1 isn't?

Answer 19

but im asking if 5/1 is an integer,. i know that if you simplify it .. it will be 5 which is an integer.. but im confuse because i know that 5/1 is a fraction.. and the definition says that an integer is not a fraction.

Answer 20

Okay... you know what a rational number is?

Answer 21

yes..

Answer 22

@meyjoux
Think of them in this manner instead:
Assuming you've mastered reducing fractions to lowest terms...

Given any fraction
If in its lowest terms, the denominator is either 1 or -1
it is an INTEGER

No buts :P

Answer 23

meyjoux keeps saying: the definition says that an integer is not a fraction.

I am curious were this definition is coming from.

A better definition for an integer might be: all fractions that can be simplified to a denominator of 1. But even that is a bit sloppy since it might invoke circular logic :)

is 9/3 an integer? 9/3 = 3/1 ... so it IS an integer.

Answer 24

an integer is any number that can be represented in simplest form as:

{...,-3,-2,-1,0,1,2,3,....}

Answer 25

http://www.techterms.com/definition/integer

Answer 26

click that to see where im getting that definition :)

Answer 27

@amistre64

Answer 28

http://en.wikipedia.org/wiki/Integer

Answer 29

and also in that link

Answer 30

from the first link: "However, when one integer is divided into another, the result may be an integer or a fraction. For example, 6 divided by 3 equals 2, which is an integer, but 6 divided by 4 equals 1.5, which contains a fraction."

so it is saying that certain fractions are integers if they simplify into an integer.


and from the wiki link: "An integer is a number that can be written without a fractional or decimal component."

The operative phrase being "CAN BE" written ... not "MUST BE" written.

Answer 31

thanks @amistre