Just how many infinities are there?

Question

OK, keep it simple!!!!
Pi is an infinite series of numbers, but it never reaches 3.15
A Third as a decimal (is this just a problem of the base 10 system?)
Think of a number, then add 1

Answer 1

Quite simply, there are an infinite number of different infinities.

There are infinite limits: these describe how a function acts as either the variable gets larger (positive infinity) or smaller (negative infinity). In a sense, there are 'potential' infinities rather than actual infinities.

There are infinities associated with counting: The size of the set of counting numbers is smaller than the size of the set of real numbers, but the same as the size of the set of even numbers. This is called cardinality. It turns out that for any set S, the collection P(S) of all subsets of S is a set that is larger in the sense of cardinality. So we can get a heierarchy with S,P(S), P(P(S)), P(P(P(S))), etc. If we start with S as the set of counting numbers, this gives an infinite collection of infinite sizes.

There are infinities associated with ordering. These are called ordinal numbers. Again, there is an infinite heierarchy of infinite ordinalities and these are different than cardinalities.

Answer 2

Repeating decimal values from rational number IS a problem with the decimal system.

If we are using base 3 number system, 1/3 would be simply 0.1

Similarly, if we were using a hypothetical base pi numbering system, pi would be equal to exactly 1

I dont really understand what youre asking. There are an infinite number of decimal numbers that can be squeezed in between any two other decimal numbers.

The problem with how some numbers appear to be inexact in decimal form is entirely because of the numbering system.

Answer 3

Pi is a real number. A real number is a number which cannot be expressed as fractions.. There are countably many fractions, but uncountably many real numbers, called the continuum. It is not because of the base 10 system.

Answer 4

There are, literally, an infinity of infinities.

You can have a one-dimensional infinity, for example, the length of the boundary of a 2D fractal shape. You can have a two-dimensional infinity, for example, the surface area of a 3D fractal shape. You can have a three-dimensional infinity, such as the volume of a 4D fractal shape. And so on...

Answer 5

e (Euler's number) is an infinite series of numbers...

2.somesthing...

√2 is another... (If you write it in decimal form)