The complex number system (differences between rational, integer, natural etc). (1 Viewer)

[x.Exhaust.x]

So what are the differences between:

1. Real numbers.
2. Rational numbers.
3. Integers.
4. Natural numbers.
5. Irrational numbers.

They seem to be common in Induction questions. Thanks.

 

[untouchablecuz]

So what are the differences between:

1. Real numbers.
2. Rational numbers.
3. Integers.
4. Natural numbers.
5. Irrational numbers.

They seem to be common in Induction questions. Thanks.

the set of real numbers contains the subsets of the rationals and the irrationals

rational numbers are numbers that can be expressed in the form p/q, where p and q are integers

irrational numbers are numbers that cannot be expressed in the form p/q, where p and q are integers

the integers are a subset of the rationals - they are natural numbers ("whole numbers" or "counting numbers") and their respective negatives

 

[kwabon]

So what are the differences between:

1. Real numbers.
2. Rational numbers.
3. Integers.
4. Natural numbers.
5. Irrational numbers.

They seem to be common in Induction questions. Thanks.

integers; -infinity, ...., -3,-2 ..... 0 ..1,2,3,...100..101,102,103...infinity
Rational numbers; a/b where a and b are integers, b=/=0
natural numbers, any integer greater than zero
irrational numbers; numbers which cannot be made into fractions, such as Root5, Root2, and so on. (simpler terms, cannot be denoted as a/b where a and b are integers)
Real numbers; include all this crap

hope it helps.


Edit: untouchablecuz beat me to it.

 

[x.Exhaust.x]

Thx untouchablecuz and kwabon .

 

[vds700]

integers; -infinity, ...., -3,-2 ..... 0 ..1,2,3,...100..101,102,103...infinity
Rational numbers; a/b where a and b are integers, b=/=0
natural numbers, any integer greater than zero
irrational numbers; numbers which cannot be made into fractions, such as Root5, Root2, and so on. (simpler terms, cannot be denoted as a/b where a and b are integers)
Real numbers; include all this crap

hope it helps.


Edit: untouchablecuz beat me to it.

slight correction- +/-infinity are not real numbers hence not included in the set of integers.

 

[cutemouse]

I don't think infinity is a real number as it does not exist.