Question

Can fractions still be considered natural, whole, integers, rational, irrational, or real numbers?

Answer 1

question is not clear.....
however, your answer cud be hidden in the following explanations:
all natural numbers are fractions but not all fractions are natural numbers
all whole numbers are fractions but not all fractions are whole numbers
only zero and positive integers are fractions but not all fractions are integers
all fractions are rational numbers but not all rational numbers are fractions
all fractions are part of set of real numbers

Answer 2

That's close, but not quite. By it's very definition, all rational numbers are all numbers that can be represented as a fraction. It may not seem like they are at first, however, because the integers would just be represented by #/1.
So no, the set of fractions cannot be contained by either the integers, the natural numbers, or the set of strictly irrational numbers. The set of all numbers that can be represented as a fraction is exactly what the rational numbers are. The rational numbers are a subset of all real numbers.

Answer 3

@mancub
You r making a very elementary but serious mistake.....
Fractions are numbers which can be represented in the form p/q, where p and q are WHOLE NUMBERS and q is not zero

Rational numbers are numbers which can be represented in the form p/q where p and q are INTEGERS and q is not zero

So your saying " all rational numbers are all numbers that can be represented as a fraction." is wrong.......
all fractions are rational numbers but NOT ALL rational numbers are fractions....☺

Answer 4

Whole numbers and integers are the same thing. :)

Answer 5

Oh wait, I see. There is no mathematical definition for whole number. So some refer to it as the natural numbers, or the natural numbers except zero. The definition I know is that they are all the numbers with no fractional remainder, ie, the integers.

Answer 6

see....
natural numbers : 1,2,3,4,........
whole numbers : 0,1,2,3,4,........ (i.e. natural numbers plus zero)
integers : .......... -4,-3,-2,-1, 0, 1, 2, 3, 4,.......... (i.e. whole numbers plus negative numbers)

I think there is some confusion in your mind regarding number systems. The above explanation will help u clear your doubts.....

Answer 7

@Harkirat

I think there is some confusion in YOUR mind regarding number systems.

Answer 8

@estudier
Pls be kind enough to point out where my knowledge about number systems is lacking. I'll be glad for you help in overcoming the lacuna.........
i would especially like to know how whole numbers and integers are one and the same thing and fractions and rational numbers are one and the same thing.....

Answer 9

you are defining whole numbers as Naturals plus 0, please provide a reference for this definition.

Naturals may be defined without 0, typically by number theorists, to avoid doubt it is customary to specify eg N+

For myself, I am familar with N, N+, Z and some others, but not with the set of whole numbers, would that be W?

Answer 10

Yes it is...

Answer 11

Reference?

Answer 12

Maybe this will help http://en.wikipedia.org/wiki/Whole_numbers

Answer 13

http://www.mathsisfun.com/whole-numbers.html

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

Answer 14

http://www.merriam-webster.com/dictionary/whole%2Bnumber

Answer 15

"Whole number is a term with inconsistent definitions by different authors. All distinguish whole numbers from fractions and numbers with fractional parts.

Whole numbers may refer to:

natural numbers in sense (1, 2, 3, ...) — the positive integers
natural numbers in sense (0, 1, 2, 3, ...) — the non-negative integers
all integers (..., -3, -2, -1, 0, 1, 2, 3, ...)

Answer 16

I don't know why you keep saying that there r no whole numbers...

If u start defining Natural numbers as positive integers
whole numbers as the non-negative integers etc.
then we shud not be able to find reference related to these....

Natural Numbers/counting numbers were the firs one to be used by humans to keep track of things they possessed
Then with the introduction of zero (when u hv nothing) led to the next set of numbers..
all later sets of numbers etc. developed from these.....
concept of integers did not pop-up before man started counting....

Answer 17

Just curiosity.......
In your country are they teaching kids number systems as N+, N- etc. from the time they start learning maths ???

Answer 18

I have well defined mathematical references for all my sets.

Those sets do not include the set of whole numbers.

Why do you need them? You have the naturals or the integers and you can specify with/without 0, positive or negative etc.

"Whole numbers" just causes unnecessary confusion.

Answer 19

There is a question posted by some youngster on here somewhere and one of the choices was something like "Whole numbers are integers".

Answer 20

So u r saying that in your country, as a kid u never heard of whole numbers???

Answer 21

No wonder the kids get confused. What's wrong with "natural" numbers?

Answer 22

Only in the context of something not being a fraction.

Answer 23

they cannot express the concept of not having anything at all, which is what zero does ........

Answer 24

What I am saying is why use a term "whole numbers" when you have a perfectly good alternative, "natural numbers"?

Answer 25

In either system, you need to specify whether 0 is included.

Answer 26

I guess having the set of Whole numbers is better than having to specify that a set includes zero or not or this is the set obtained after omitting negative numbers..

That way why need for integers etc.
Use the biggest set of numbers only with symbols indicating what is included and what is excluded..

As far as I am concerned, it is far more confusing for a child to understand all this exclusion and inclusion business..
Yes for a person studying advance maths at an age of 18-19 years, these things might make sense but not for young children....☺

Answer 27

My interest is not to argue with you for arguments sake.........

We are all entitled to our opinion, but in India we still learn about Whole numbers ,.........

so I based my answers on what I still think is a good way of building the number system by adding bit by bit to get bigger/higher levels......

Answer 28

I see what you mean but the basic problem remains, there is no consistent definition for "whole numbers".

Meaning a kid could go to one school and get one thing then a different school and get another.

Answer 29

Either way, to get back to the original debate, Wolfram defines a fraction the same way as a rational number, so it doesn't matter how you define whole numbers.
http://www.wolframalpha.com/input/?i=fraction+definition

Answer 30

I do not know who this wolframalpha guy is but i have seen books published in other countries having separate definitions for fractions and rational numbers

who can eat -1/2 of a cake???

in fractions p/q, p and q are whole numbers
In rational no p/q, p and q are integers...

Answer 31

all fractions are rational numbers but not all rational numbers are fractions........

Answer 32

In pure mathematics, there is no reason to have a separate definition for the two terms.

Answer 33

so u r welcome to eat -1/2 of my cake.....☺

Answer 34

That's not an example from pure mathematics.