0
Countably infinite means you can set up a one-to-one correspondence between the set in question and the set of natural numbers. It can be shown that no such relationship can be established between the set of real numbers and the natural numbers, thus the set of real numbers is not "countable", but it is infinite.
Still curious? Ask our experts.
Chat with our AI personalities
Steve
Lao
JordanAdd your answer:
Earn +20 pts
Is the set of irrational numbers countably infinite?
No. The set of irrational numbers has the same cardinality as the set of real numbers, and so is uncountable.The set of rational numbers is countably infinite.
Is there a number bigger than infinity?
No, there isn't a number bigger than infinity. Infinity is well, infinite, so it never finishes.
What is infinite and finite set in math?
A set is finite if there exists some integer k such that the number of elements in k is less than k. A set is infinite if there is no such integer: that is, given any integer k, the number of elements in the set exceed k.Infinite sets can be divided into countably infinite and uncountably infinite. A countably infinite set is one whose elements can be mapped, one-to-one, to the set of integers whereas an uncountably infinite set is one in which you cannot.
Is every measurable functions continuous?
No, a measurable function may have a finite number of discontinuities (for the Riemann measure), or a countably infinite number of discontinuities (for the Lebesgue measure). It should also be bounded (have some upper and lower bound, or limit, in the domain that is being measured), to be measureable. At least, some unbounded functions are not measurable.No, a measurable function may have a finite number of discontinuities (for the Riemann measure), or a countably infinite number of discontinuities (for the Lebesgue measure). It should also be bounded (have some upper and lower bound, or limit, in the domain that is being measured), to be measureable. At least, some unbounded functions are not measurable.No, a measurable function may have a finite number of discontinuities (for the Riemann measure), or a countably infinite number of discontinuities (for the Lebesgue measure). It should also be bounded (have some upper and lower bound, or limit, in the domain that is being measured), to be measureable. At least, some unbounded functions are not measurable.No, a measurable function may have a finite number of discontinuities (for the Riemann measure), or a countably infinite number of discontinuities (for the Lebesgue measure). It should also be bounded (have some upper and lower bound, or limit, in the domain that is being measured), to be measureable. At least, some unbounded functions are not measurable.
What does Infinite pains mean?
great effort
