The ‘lazy eight’ symbol ‘∞’ has long been used to denote the infinite since this shape can be traversed endlessly.
Till the mid 19th 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!