Integers, rational and irrational and real numbers can be either positive negative or zero?

Question

If we have a zero how can we say is it integer or is it irrational or else

I am sure that my question is correct

Second answer
Note that rational and irrational numbers are completely different.
1/2 is no at all irrational 100% sure

Answer 1

0 is an integer (I hope this is obvious to you), and since it can be expressed as 0/1 it is also a rational number (the previous poster has apparently confused 0/1 with 1/0 - 1/0 is the one you can't do, whereas 0/1 is simply 0). Note that all integers are also rational. Irrational numbers are simply all real numbers that are not rational, and since 0 is rational, it is not irrational (the previous poster got this one wrong too). 0 is, of course, a real number, as are all rational and irrational numbers (at your level, the only numbers that you will have been exposed to that aren't real are those involving i, where i is defined as √(-1). Since 0 contains no such expression, it is real).

Answer 2

You should see them as sets :
Integers are contained in Rational
Rationals are contained in irrational
Irrationals are contained in Real

1/2 is rational but not an Integer.
1/2 is also an Irrational and also a Real.

Zero is contained in the Integers thus 0 is an Integer, and a Rational and an Irrational and a Real number.

It is common practice to name a number by its most significant name, that is the name of the 'smallest' set that contains the number.
So 1/2 is called a rational, and not (although correct) a Real.

Answer 3

the magic of maths began lengthy earlier. The earliest become purely counting of 'issues'. This counting used numbers like a million, 2, 3, 4, .. and were called "organic" numbers. They were ... umm.. 'organic !! :D and human beings tried to do addition and subtraction on those. Which become commonly ok, yet now and again that they had arise with unusual consequences ... !! Like at the same time as the tried to do (5 - 7) ... there become NO thanks to position in writing the answer making use of organic numbers ?!?! so as that they went and figured that we may be able to also "count number" no longer some thing. and likewise "decrease than no longer some thing". And prolonged the organic numbers set with the aid of coming up 0, and negative numbers (gasp !) This NEW style set become given the call "actual Numbers" Then they persevered doing mathematics. including/ subtracting/ dividing/ multiplying. This time it become the branch which created hardship. Many actual numbers at the same time as divided one with the aid of yet another gave an answer which become also a actual style. Like (e.g.) 12/ 3 = 4 or -40 2/ 7 = -6. All become good. yet THEN .. there have been some which failed to offer a actual style answer ?!? Like (e.g.) 7/ 3 = ???, or 5/ 27 = ??? and so as that they created yet another more effective NEW set - called Rational numbers. From the note "Ratio". i.e. numbers that must be written because the ration of two actual numbers, yet whose answer isn't a actual style ! Then they carried on doing math. And wager what ? They got here up with equations like x^2 = 3 !! OR .. what's x ... = sqrt( 3) ?? they stumbled on you may't write this style as a ratio of two reals. NOW what to do ?!? so as that they went and calculated it in any case, yet wanting to call such numbers -- Irrational !! which ability "no longer writeable as a ratio of any 2 actual numbers". --- and that is what that is all about next Episode : extra extensions to the fashion set because of nevertheless extra issues. the arrival of Imaginary numbers, transcendental, the Very tremendous numbers etc etc. :D

Answer 4

The number zero has created endless hours of discussion, and indeed confusion.

Zero behaves differently from other numbers. The idea of zero is synonymous with absence, so I choose to view the set of all positive integers, and zero as opposite ideas rather than considering zero to be a distinct number like 1, 2 or 3. In set theory, the idea of a null (or empty) set, is a similar idea. I emphacise that it is the number zero, not the idea, that I choose to eliminate. Presence is the opposite idea of zero and in the realm of numbers, zero reflects the absence of numbers. In otherwords, something either exists, or it doesn't. If it exists, then it has a quality that we call number associated with it, and if it doesn't exist we call this absence, zero.
I will leave this discussion to the philosophers to ponder in more depth.

Answer 5

we say 2*3 melons=6 melons
we say 2*3 integer=6 integer
we say integer!=integer
then we say 0!=1=integer
hence 0 is an integer, although it has been so by definition.

Answer 6

Zero is not an integer...
Zero is not rational (0/1234 does not work)
Zero is in a way irrational, but in another it's not...