The ‘lazy eight’ symbol ‘∞’ has long been used to denote the infinite since this shape can be traversed endlessly.

Till the mid 19^th century the only concept of infinity, in the mathematical world, was linked to ‘countable numbers’ or integers or natural numbers – as they are commonly known. As we count we go:-

1, 2, 3, 4,…..n…….. ∞    (‘natural numbers’)

Here ‘n’ stands for any countable integer. At the end of this seemingly endless sequence the number becomes too large to count and is denoted normally by ‘∞’. Cantor called this set א₀ (Aleph–nought) a “countable infinite set”. Now obviously if we add or subtract any number from א₀ it remains unchanged i.e. א₀ +1 = א₀

Not only this א₀ + א₀ is just א₀: this is the very definition of infinity!

The earliest limitation of this way of thinking was probably expressed by Euclid (330–275 BC) when he tried to answer the question – “How many points are there in a ‘line segment’?” Now a line is a ‘line’; it is continuous and how can we talk about it as ‘discrete’ points? But then, that is what mathematicians are all about; they question what seems obvious and keep building a pyramid of well-grounded higher knowledge. In fact Euclid’s axioms and theorems are even today part of elementary school Geometry. But he could not answer this one!