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The knoweledge has evolved. We know more than what we knew yesterday.It has branched off into many different areas.It has created many concepts .... and all of those concepts can be learned by any newcomer.But some of the concepts are abstract , purely abstract.How can one learn these creations of mind if they do not suggest any thing real ?For example infinity , 0 , complex number i , extended number systems which allow divisions and multiplication of infinity .Can we(or should we) define them in a way which purely abstract?If not then how will we define the conpcepts mentioned above?
I am referring to the Extended Real Numbers which includes infinity as a Number.When you say 2people +3 people = 4 people there is a evolutionary link with the method of empirical understanding to understand an abstract idea using associations with real world instances. people are real .. they are not abstract .And the real objects found in nature are used to develop a understanding of addition.infinity , 0 and i are simple from the point of evolutionary thought. Try to define infinity , 0 or i to a student without using purely Abstract constructs. To begin with , suppose a person who doesnt understand Numbers asks :What is Number? What will be your answer?