How do you compare two infinity?

If functions f(x) and g(x) tend to infinity as x tends to infinity then the limit f(x)/g(x) = L is an indeterminate form comparing infinities. If L is infinity then f(x) is huge compared to g(x). If L is 0 then g(x) is huge compared to f(x). If L is some other number then both are of same order except for a factor.

Can two infinities be compared?

After he established that the sizes of infinite sets can be compared by putting them into one-to-one correspondence with each other, Cantor made an even bigger leap: He proved that some infinite sets are even larger than the set of natural numbers. Thus, a second kind of infinity was born: the uncountably infinite.

How are there different infinities?

As German mathematician Georg Cantor demonstrated in the late 19th century, there exists a variety of infinities—and some are simply larger than others. These numbers are unbounded, and so the collection, or set, of all the natural numbers is infinite in size.

How do you measure infinity?

Infinity is not a real number, it is an idea. An idea of something without an end. Infinity cannot be measured.

Can infinities be bigger than others?

Yes. If you’re given an infinite set, there is a simple method to make a larger infinity: take its power set, which is always of higher cardinality. So not only some infinities are larger than others, but there is no a “largest” inifinity, you can always create a larger one.

How many infinities are there?

There is more than one ‘infinity’—in fact, there are infinitely-many infinities, each one larger than before!

Why is infinity important in math?

Infinity is often used in describing the cardinality of a set or other object (such as a list or sequence of terms) that does not have a finite number of elements. The concept of infinity is extremely important in a variety of contexts, most notably calculus and set theory.

Is countable infinity higher than uncountable infinity?

(a) Yes, every uncountable infinity is greater than every countable infinity.