Partial preview of the text
Download mathematical induction proof sumaary and more Summaries Discrete Mathematics in PDF only on Docsity!
PRINCIPLE OF MATHEMATICAL INDUCTION Pr “Analysis and natural philosophy owe their mos this fruitful means, which is called induction. Newton w to it for his theorem of the binomial and the principle of _ universal gravity. — LAPLACE *# { important discoveries to as indebted 4.1 Introduction One key basis for mathematical thinking is deductive rea- soning. An informal, and example of deductive reasoning, borrowed from the study of logic, is an argument expressed in three statements: (a) Socrates is a man. (b) All men are mortal, therefore, (c) Socrates is mortal. If statements (a) and (b) are true, then the truth of (c) is established. To make this simple mathematical example, we could write: @) Eightis divisible by two. (i) Any number divisible by two is an even number, G. Peano therefore, (1858-1932) ii) Eight is an even number. _ Thus, deduction in a nutshell is given a statement to be proven, often called a conjecture or a theorem in mathematics, valid deductive Steps aan owed and a f ; 7 . Vy proof may or may not be established, i.e., deduction is the applicati ral case to a particular case. PP ion of a gene In contrast to deduction, inductive re i : , asoning depends on worki i : . orking with each case- and develope a Feveentty by observing incidences till we have dhaceved each and every case. It is Tequently used in mathematics and is a ke f scientific reasoning, where ot inact and analysing data is the notin tine aspect 1 a ase ve can say the w i . in simple lan , we y the word induction means the generalisation from particular a or facts. CamScanner 
