Infinity

The concept of infinity is introduced to children right from grade 1!

The first math skills children learn is counting and counting can raise many queries in their mind, though they may not have the language skill to express them.

They learn counting up to 10 and then 100 & then 1000.

They also learn that there is no "biggest" number. and that given any number, they can find a number greater than that number.

Fractals are a way of understanding infinity. A fractal shape can be zoomed continuously to show more details and similar patterns.

Countable & Uncountable Infinities

While thinking deeply about infinity, Georg Cantor realised that "the points within a mere line segment could indeed correspond to every point in three-dimensional space."

In 1874 he proposed that there are 2 types of infinities: a “countable infinity”, and an “uncountable infinity”.

A countable infinity is the one for which we can actually “count” all its elements by natural numbers (i.e. 1, 2, 3, 4, …). An uncountable infinity is one which cannot be counted in the above manner.

He proved that even, odd, squares, cubes and even all rational numbers were countable.

Irrational & real numbers were uncountable.

His proof was based on the principle of "one to one correspondence" which is one of the first math principles which children learn!

For uncountable infinities the infinity of whole numbers would not be sufficient to count them. In a sense they have more elements than countable infinities.

Infinity in Math

The entire topic of calculus was built on the notion of infinity.

An interesting example of a series containing an infinite number of terms but which has a finite sum.

The best example is that of 1 + 1/2 + 1/4 +.... which has an infinite number of terms, each subsequent term being half the value of the previous one. It has a total of 2! This series can be understood visually also.