How do we know some numbers, like Pi are endless, instead of just a very long number?

We know that some numbers , like Pi , are infinite because we have proven it mat hem atically . Pi is the ratio of a circle ' s circum ference to its diameter , and it is an irr ational number , meaning it cannot be expressed as a simple fraction . This means that the decimal representation of Pi goes on in def initely without repe ating . \n \n One way to prove that Pi is infinite is through the proof by contrad iction . We assume that Pi is a finite number , and we try to find a contrad iction . For example , we can use the fact that the circum ference of a circle is always greater than its diameter to show that Pi cannot be a finite number . \n \n An other way to prove that Pi is infinite is through the use of mathematical form ulas and equations . For example , we can use the fact that the sum of the angles in a triangle is always 1 8 0 degrees to show that Pi is infinite . \n \n Over all , the proof that Pi is infinite is based on mathematical reasoning and logic , and it has been verified by mat hem atic ians and scientists for centuries . </s>