Podcast
Questions and Answers
संख्याओं के स्थानिय प्रमाण का प्रयोग किस प्रकार किया जाता है?
गणितीय प्रमाण का सिद्धांत
गणितीय प्रमाण का सिद्धांत क्या है?
यदि आप एक आधार मामान के लिए साबित कर सकते हैं और फिर सिद्ध कर सकते हैं कि हर बार जब यह किसी संख्या x के लिए सत्य है, तो यह x+1 के लिए भी सत्य होगा, तो आप जानते हैं कि यह आपके पहले आधार मामान के बाद सभी संख्याओं के लिए सत्य होगा।
आधार मामान किसे कहते हैं?
किसी संख्या के लिए सत्य होने को साबित करने के लिए
गणितीय प्रमाण के सिद्धांत का उपयोग कहाँ होता है?
Signup and view all the answers
गणितीय प्रमाण का उपयोग किसके लिए विशेष रूप से उपयोगी है?
Signup and view all the answers
Study Notes
Mathematical induction is a powerful proof technique used by mathematicians to prove statements that involve positive integers. It relies on the principle of mathematical induction: if you can show that a statement holds true for one base case, and then prove that every time it's true for some number x, it must also be true for x+1, then you know it will be true for all numbers after your first base case. In other words, we start with our initial condition (the base case), then assume that the statement is true up until some particular point in the sequence of integers, and finally show that this leads to the conclusion that the statement must hold for all subsequent points in the sequence. This process is especially useful when trying to prove properties true for large sets of integers, like showing that addition is commutative or associative over the entire set of integers.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Learn about the powerful proof technique of mathematical induction used to prove statements involving positive integers. Understand the process from establishing a base case, assuming truth up to a certain point, and logically concluding its truth for all subsequent points in the sequence.
