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1. No.
The Natural numbers are the positive integers (sometimes the non-negative integers).
Rational numbers are numbers that can be expressed as the quotient of two integers (positive or negative). All Natural numbers are in the set of Rational numbers. 2. No. Natural numbers are usually defined as integers greater than zero. A Rational number is then defined simply as a number that can be expressed as an integer divided by a natural number. (This definition includes all rational numbers, but excludes division by zero.)
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Why is every rational number a real number?
There are rational numbers and irrational numbers. Real numbers are DEFINED as the union of the set of all rational numbers and the set of all irrational numbers. Consequently, all rationals, by definition, must be real numbers.
Are natural numbers the same of rational numbers?
The set of rational numbers includes the set of natural numbers but they are not the same. All natural numbers are rational, not all rational numbers are natural.
Is the set of all real numbers continuous and the set of all integers discrete?
Yes, every Cauchy sequence of real numbers is convergent. In other words, the real numbers contain all real limits and are therefore continuous, and yes the integers are discrete in that the set of integers only contains (very very few, with respect to the set of rationals) rational numbers, i.e. their values can always be accurately displayed unlike the set of reals which is dense with irrational numbers. It's so dense with irrationals in fact, that by comparison, the set of rationals can be called a null set, however that is a different topic.
What is a set of numbers including zero and all the counting numbers?
Whole numbers are the set of natural or counting numbers inclding zero
Does the set of rational number overlap the set of irrational numbers why?
By definition, the two sets do not overlap. This is because the irrationals are defined as the set of real numbers that are not members of the rationals.
Are there more rational number than irrational numbers?
There are more irrational numbers than rational numbers. The rationals are countably infinite; the irrationals are uncountably infinite. Uncountably infinite means that the set of irrational numbers has a cardinality known as the "cardinality of the continuum," which is strictly greater than the cardinality of the set of natural numbers which is countably infinite. The set of rational numbers has the same cardinality as the set of natural numbers, so there are more irrationals than rationals.
What is the set of all numbers containing zero as well as all postitive and negative numbers?
The answer depends on what do you mean by "all". It could be the set of all integers, the set of all rationals or the set of all reals.
The number -4 is what set of numbers?
The number -4 belongs to the set of all integers. It also belongs to the rationals, reals, complex numbers.
What is a set of rational numbers that begin at 0?
It could be the set denoted by Q- (the non-positive rationals) or Q+ (the non-negative rationals).
Why is every rational number a real number?
There are rational numbers and irrational numbers. Real numbers are DEFINED as the union of the set of all rational numbers and the set of all irrational numbers. Consequently, all rationals, by definition, must be real numbers.
What numbers are in the set of natural numbers and which are in the set of whole numbers?
All of the natural numbers.
What set of numbers does -23 belong to?
Integers, rationals, reals, complex numbers, etc.
Are natural numbers the same of rational numbers?
The set of rational numbers includes the set of natural numbers but they are not the same. All natural numbers are rational, not all rational numbers are natural.
What represents fractions?
Q represents the set of all rational numbers, Zrepresents the set of all integers so Q excluding Z, represents all rationals that are not integers.
Is the set of all real numbers continuous and the set of all integers discrete?
Yes, every Cauchy sequence of real numbers is convergent. In other words, the real numbers contain all real limits and are therefore continuous, and yes the integers are discrete in that the set of integers only contains (very very few, with respect to the set of rationals) rational numbers, i.e. their values can always be accurately displayed unlike the set of reals which is dense with irrational numbers. It's so dense with irrationals in fact, that by comparison, the set of rationals can be called a null set, however that is a different topic.
What are all of the natural numbers that are not integers?
Null set. All natural numbers are integers.
How are irrational numbers abbreviated?
There is not a specific abbreviation. The set is denoted by R - Q: the real numbers minus the rationals.
