what is meant by real numbers?

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what is meant by real numbers?

Mathematics
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Do you know limits?
The field of all rational and irrational numbers is called the real numbers

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Can you explain irrational numbers other than saying they are the non-rational real numbers?
an irrational number is any real number which cannot be expressed as a fraction a/b...
Yeah, that does not explain, what real numbers are!
so u understand wt an irrational no is
I'm just saying, that the original question was, what a real number is, and you can't explain it by saying "A real number is a real number (which is rational or not).". But it seems sarav is not interested anymore.
if u do knw wt a rational and irrational no is...then it is quite simple to understand wt real no is.. then the question is do u knw wt a rational or irrational no is
That was the other point a made: You can not know what irrational numbers are, until you know what real numbers are. So there is no use in bringing them up when explaining real numbers in turn!
A real number is a number that holds a position on a number line from negative infinity to poitive infinity
actually this is a very deep question, and not at all easy to understand. if you are asking "what does my teacher mean when referring to real numbers? then it is pest thought of a points on a number line
if you are asking what "mathemeticians" mean when they talk about "the real numbers" then there is a lot to be said and learned. see for example http://en.wikipedia.org/wiki/Real_number
this question is used to trip up graduate students on oral exams. it is very hard to answer.
you can research dedikind cuts if you have the patience \http://en.wikipedia.org/wiki/Dedekind_cut
I'm not sure that questions are posed to trip up students it sort of implies the examining body wants the student to fail.
satellite73: That's why I asked the inquirer whether she understands limits, because otherwise you don't need to know the difference between real and rational numbers.
but if you are asking because you hear people say "real number" it is a synonym for "all numbers" and you can think of points along a number line.
gianfranco, i am sure of it.
Ok i respect your opinion.
a real number is a number that exists. it can be an integer, decimal, rational or irrational number.
I don't know a way to define "exists" other than saying, a line of that length can be constructed just with compass and straight-edge. Even if you allow other units, like length of curved lines, I'm quite sure not all real numbers can be constructed. Also this is a very impractical definition. In particular it makes it impossible to show that the real numbers are a complete topological space, which is what you really in mathematics. Fortunately mathematics doesn't rely on philosophical definitions.

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