“Mathematical induction, which is purely ordinal... may be stated as follows: A series generated by a one-one relation, and having a first term, is such that any property, belonging to the first term and to the successor of any possessor of the property, belongs to every term of the series.”
“Few contemporaries were as profoundly read in the history of mathematics as was De Morgan. No subject was too insignificant to receive his attention. ...In [his] article "Induction (Mathematics)," fir...”
Mathematical induction
“One who extended the theory of equations somewhat further than Vieta was Albert Girard... Like Vieta this ingenious author applied algebra to geometry, and was the first who understood the use of nega...”
Mathematical induction
“A more modern attempt to explain the fruitfulness of mathematical reasoning is that of Poincaré, who finds it all due to the principle of mathematical induction. This principle of mathematical inducti...”
Mathematical induction
“It is absolutely certain that if a proposition is established by mathematical induction, it will never be disproved, i.e., if a general proposition is true of n + 1 whenever it is true of n,...”
Mathematical induction
“We can not... escape the conclusion that the rule of reasoning by recurrence is irreducible to the principle of contradiction. ...Neither can this rule come to us from experience... This rule, inacces...”
Mathematical induction
