If you read Bertrand Russell who devoted his life for search of proper definitions of basic terms of science you would know. He could not find them - his definition of number boiled down to so-called paradox of Russell - description of object is called normal when one don't use this object as its element.
Take defintion of number - it is multitude of multitudes which is equivalent to some exemplary multitude (Sorry for bad English, it is in back translation). But one cannot define this exemplary multitude. So it means mathematicians have no definition of number without using tautology.