Venlo Mac Van
No. Fractions do not include irrational numbers. And although there are an infinite number of both rationals and irrationals, there are far more irrational numbers than rationals.
I don't understand what you mean by deeper, but the cardinality of irrational numbers, Aleph-One, is greater than the cardinality of rationals, Aleph-Null. That is to say, there are more irrational numbers than rationals. [If you treat infinity as a number, there are infinity to the power of infinity irrational numbers compared with "just infinity" for rationals.]
Starting at the top, we have the real numbers. The rational numbers is a subset of the reals. So are the irrational numbers. Now some rationals are integers so that is a subset of the rationals. Then a subset of the integers is the whole numbers. The natural numbers is a subset of those.
Natural numbers.
Yes. There are infinite whole numbers, and whole numbers are rational.
No. Fractions do not include irrational numbers. And although there are an infinite number of both rationals and irrationals, there are far more irrational numbers than rationals.
The number of rationals is Aleph-null.
I don't understand what you mean by deeper, but the cardinality of irrational numbers, Aleph-One, is greater than the cardinality of rationals, Aleph-Null. That is to say, there are more irrational numbers than rationals. [If you treat infinity as a number, there are infinity to the power of infinity irrational numbers compared with "just infinity" for rationals.]
Starting at the top, we have the real numbers. The rational numbers is a subset of the reals. So are the irrational numbers. Now some rationals are integers so that is a subset of the rationals. Then a subset of the integers is the whole numbers. The natural numbers is a subset of those.
YES
Natural numbers.
Negative integers, rationals and real numbers
Integers, rationals, reals, complex numbers, etc.
Yes. There are infinite whole numbers, and whole numbers are rational.
It could be the set denoted by Q- (the non-positive rationals) or Q+ (the non-negative rationals).
Yes. Rational numbers are numbers that can be written as a fraction. All rationals are real.
Natural (or counting) numbers Integers Rationals Irrationals Transcendentals