# Is Pi in mathematics really infinite or is science not yet over calculated and talked about?

The notion of finite or infinite is something other than that you probably mean.

A finite number [MATHX [/math is bounded.That is, we can choose an integer [Mathn [/math so that the absolute value of [MATHX [/math Is Smaller than [MATHN [/math].

Because we know for sure that [math | \\pi | < 4 [/math applies that [MATH\\PI [/math is finite.

Something else is that you cannot write [math\\pi [/math by using a finite number of decimal places (digits after the decimal point).

This is not an exciting trait in itself, you have seen that:

[math1/11 \\approx 0.09090909… [/math.Even with natural numbers, you may not be able to write down the answer exactly with a finite number of digits after the comma.

For [MATH\\PI [/math It also applies that it has an infinite number of decimal digits, but these figures are more special, because unlike my previous example, these figures do not repeat themselves in a fixed pattern.

We therefore know for sure that [MATH\\PI [/math does not write as a fracture of [math2 [/math natural numbers, or with math notation [math\\pi\\notin \\mathbbq [/math or in words [MATH\\PI [/math is not Rational.

We also know for sure that [MATH\\PI [/math is not a solution of an algebraic equation.A number for which it is valid is [math\\sqrt 2 [/math.For instance, [math\\sqrt 2 [/math is a solution of [Mathx ^ 2 -2 = 0 [/math, a polynom of the second degree.We call [math\\sqrt 2 [/math algebraic.This kind of equation is for [MATH\\PI [/math so not to be found.

We call [MATH\\PI [/math ] transcedent.That means [MATH\\PI [/math is not a solution of an algebraic equation.

The short answer is that science is already here. Incidentally, I always write “We know/We call”, but the proof that [MATH\\PI [/math has all these properties is not that very simple.

Finally, for clarity.A very large number is also finite. Even a number for which you need for example 1 year, or all your life, to write down all the digits.

You mean I suppose the number of decimal places is infinite or not?

The scholars do agree: “蟺 is an irrational number, meaning that it cannot be written as the ratio of two integers (fractions such as 22/7 are commonly used to approximate 蟺, but no common fraction (ratio of whole numbers) can be its exact value).

Because 蟺 is irrational, it has an infinite number of digits in its decimal representation“