Question

0 is a natural, whole, and integer?

Answer 1

theres debate as to its natural state; so youll have to be source specific there

Answer 2

Good on granola as well.

Answer 3

I'm not sure about 0 being natural

Answer 4

my teachers always say; "im grading the test, so it needs to be my definitions" :)

Answer 5

very popular this question. i like to think of zero this way

Answer 6

integer too

Answer 7

0 is an element of the whole numbers
and
an element of the integers

natural numbers are your counting numbers
you don't start counting with 0

Answer 8

i do

Answer 9

so whole integer and irrational?

Answer 10

0 is the integer immediately preceding 1. In most cultures, 0 was identified before the idea of negative things (quantities) that go lower than zero was accepted. Zero is an even number,[21] because it is divisible by 2. 0 is neither positive nor negative. By some definitions 0 is also a natural number, and then the only natural number not to be positive. Zero is a number which quantifies a count or an amount of null size.

Answer 11

sure you do satellite
i acutally start counting with -1

Answer 12

I like to count starting from 0

Answer 13

0 isn't irrational
its rational since we can write 0 as a fraction of integers like 0/4

Answer 14

isnt 0/4 mean it empty?

Answer 15

0/4=0

Answer 16

0/a=0 as long as a does not equal 0

Answer 17

so 0 cant be natural and irrational? even though natural seems to fit it?

Answer 18

0 is natural ,rational,integer

Answer 19

i don't think zero is actually a number. i think it is nothing

Answer 20

its not natural

Answer 21

they don't have that option

Answer 22

yy?

Answer 23

its not irrational
its rational

Answer 24

wat r the options?

Answer 25

Ok, so seriously it is definitely whole, definitely an integer. But it usually considered not a natural number.

For the record, it is emphatically a rational number.

Answer 26

it is whole number and integer

Answer 27

yes and rational and real and complex

Answer 28

it is natural BY SOME DEFINITIONS.

Answer 29

its natural by false definitions

Answer 30

http://en.wikipedia.org/wiki/0_(number)

Answer 31

irrational or integer,rational or natural, whole, integer or whole, integer, rational

Answer 32

i will never include 0 in the natural numbers

Answer 33

"whole, integer, rational"

Answer 34

i don't care what book says its natural
its a lie

Answer 35

yep JAmesJ

Answer 36

ok thank you still confuses me should be natural to

Answer 37

why don't computer science people just say whole numbers instead of steeling math people's terms to define their sets

Answer 38

no should not be natural lol

Answer 39

see 1st commetn on this ques

Answer 40

allot of comments for thisquestion

Answer 41

first one

Answer 42

by amistre

Answer 43

oh

Answer 44

if you are taking a math class
then its not a natural number
if you are taking a computer science class
then people in this group like to make up stuff like 0 being natural

Answer 45

oh i see

Answer 46

make up stuff????????????????????????????????

Answer 47

A much later advance was the development of the idea that zero can be considered as a number, with its own numeral. The use of a zero digit in place-value notation (within other numbers) dates back as early as 700 BC by the Babylonians, but they omitted such a digit when it would have been the last symbol in the number.[1] The Olmec and Maya civilizations used zero as a separate number as early as the 1st century BC, but this usage did not spread beyond Mesoamerica. The use of a numeral zero in modern times originated with the Indian mathematician Brahmagupta in 628. However, zero had been used as a number in the medieval computus (the calculation of the date of Easter), beginning with Dionysius Exiguus in 525, without being denoted by a numeral (standard Roman numerals do not have a symbol for zero); instead nulla or nullae, genitive of nullus, the Latin word for "none", was employed to denote a zero value.[2]
The first systematic study of numbers as abstractions (that is, as abstract entities) is usually credited to the Greek philosophers Pythagoras and Archimedes. Note that many Greek mathematicians did not consider 1 to be "a number", so to them 2 was the smallest number.[3]
Independent studies also occurred at around the same time in India, China, and Mesoamerica.
Several set-theoretical definitions of natural numbers were developed in the 19th century. With these definitions it was convenient to include 0 (corresponding to the empty set) as a natural number. Including 0 is now the common convention among set theorists, logicians, and computer scientists. Many other mathematicians also include 0, although some have kept the older tradition and take 1 to be the first natural number

Answer 48

i like that you include footnotes in your replies; but have no actual footnotes to reference lol

Answer 49

well .......

Answer 50

I agree with myininaya. 0 is not a natural number. That is why we have the whole numbers.

Answer 51

sorry i made you guys argue =/just needed help with my math homework and it turned into a long topic

Answer 52

in their defense; it does seem rather contrived to make up a whole new set just so that we include zero .....

Answer 53

Zero is also very much alike to the other natural numbers in that it is a nonnegative integer. The possible weirdness of zero pales in comparison to the weirdness of negative numbers. Read any reputable algebra text of fifteenth century Europe to see the great pains they go through to avoid mentioning negative numbers, and you will see what I mean. Even as late as the nineteenth century, kooks like Leopold Kronecker devised roundabout ways to avoid mentioning negative numbers (I don't believe he ever specified either if he included zero when he said "God created the natural numbers; everything else is the work of Man.").

Its primitiveness is another good reason to include it among the natural numbers. It's the additive identity, for crying out loud; anything plus zero stays the same. If you include zero among the natural numbers you have a monoid, one of the minimally interesting algebraic sets. Furthermore, when building numbers out of set theory as they enjoyed doing it during the early twentieth century, the only set that we seem certain enough that should exist by itself to merit its own axiom of existence is the empty set. It's the only natural place to start, and zero of course gets identified with the empty set. All other natural numbers, as sets, can be built out of the empty set! Zero, if it belongs anywhere, belongs with the natural numbers.

Answer 54

wow so much to read did u type that all out?

Answer 55

if i plug this into "turn it in" :)

Answer 56

@remoore not surprising since zero has a long and tortured history. even in the moder era apparently. i for example don't except its existence, although i use it frequently

Answer 57

nope

Answer 58

well ima call 0 a natural number since its on a number line and aint a fraction

Answer 59

yeahhh
I win

Answer 60

that would be good if you could keep it consistent; but then again, negative numbers are on the number line and aint fractions

Answer 61

0 aint a negative though

Answer 62

if you could devise a system that is consistent with your definition, then by all means :)

Answer 63

lol