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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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Q: Are All rationals numbers are in the set of natural numbers?

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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.

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.

The set of Natural numbers.

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.

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.

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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.

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.

The number -4 belongs to the set of all integers. It also belongs to the rationals, reals, complex numbers.

All of the natural numbers.

It could be the set denoted by Q- (the non-positive rationals) or Q+ (the non-negative rationals).

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.

Integers, rationals, reals, complex numbers, etc.

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.

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.

No.

0 and negative integers are all whole numbers but they are not natural numbers.

The set of integers, Z.

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