I am learning mathematical analysis. In one of the pages of a book on analysis I found a statement which I could not digest. The statement was "Cantor constructed $\mathbb R$ using nested intervals". Another such statement was "Dedekind constructed $\mathbb R$ out of $\mathbb Q$ using his ideas of Dedekind cuts".
Could you, my fellow users, kindly explain what is the meaning of this statement? Is "construction" having some indispensable mathematical definition? If the answer to the second question comes in positive then I will be grateful if somebody puts up the definition.