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Zainab
If one book falls on the shelf then all the books will fall one by one.

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AYESHA
Mathematical induction proves that we can climb as high as we like on a ladder, by proving that we can climb onto the bottom rung (the basis) and that from each rung we can climb up to the next one (the step).

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zafreen -

All biological life forms that we know of depend on liquid water to exist.

Therefore, if we discover a new biological life form it will probably depend on liquid water to exist.

A classical example of an incorrect inductive argument was:

All of the swans we have seen are white.

Therefore, we know that all swans are white.

The correct conclusion would be, "We expect that all swans are white".””

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Another example is that of knowledge. If we share our knowledge with somebody and make sure that that person will share it with another person then infinite number of people will benefit from that knowledge.NASHITA

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Christina  Principle of mathematical induction is an excellent proof strategy that can be used to prove statements & theorems which are otherwise difficult or impossible to prove. Hence, it is used widely in theoretical computer science subjects such as Discrete Mathematics & Automata theory.  Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them.

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Meera-

The few practical examples of mathematical induction are :

1: To prove that if dominoes are arranged in the manner given below , if first one falls then all the dominoes will fall.

If the first domino is pushed down it will fall, so the base of induction is true. For a general ‘k’ th domino , if it falls it will cause the next domino to fall. Hence, it can be proved that pushing the first domino will cause to fall all the dominoes in the queue.

2. To prove that we can successfully zip a proper zipper if the first teeth of zip is zipped successfully

If the first teeth is closed successfully the base of induction method is true. A proper zipper, zips the next teeth successful. So if ‘k’ th zip is successfully closed then the zipper will successfully close the next teeth. The value of ‘k’ can be any arbitrary value between first and last teeth of the zipper. Thus, it can be proved that the zipper will be successfully zipped.

Similar to these example it has variety of practical applications.

3)Consider a long circular road that has a number of fuel depots along the way. All in all, the depots contains just the right amount of fuel to get your car around. You start with an empty tank. Show that you can always find a depot at which to start so that it's possible to get all the way round.

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Nashita: In a stampede when one person falls , it leads to everybody falling

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Arpita Roy : Deductive reasoning is often used in maths to makes inferences in science, as you must use formal logic to support a conclusion or a solution. An essential component of statistics, research and probability, inductive reasoning supports us in identifying patterns and making better decisions in the workplace.  An example of an argument using deductive reasoning:

All men are mortal.

Socrates is a man.

Therefore, Socrates is mortal.

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To prove that we can successfully zip a proper zipper if the first teeth of zip is zipped successfully

If the first teeth is closed successfully the base of induction method is true. A proper zipper, zips the next teeth successful. So if ‘k’ th zip is successfully closed then the zipper will successfully close the next teeth. The value of ‘k’ can be any arbitrary value between first and last teeth of the zipper. Thus, it can be proved that the zipper will be successfully .

-nandana

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Ardra:

Recursion is a term that is used often in computer science. It is a method where the solution to a problem depends on solutions to smaller instances of the same problem. The program tested whether the  input argument was some basis case like 1 or 2. If not, you solved the bigger case by breaking it into pieces and calling the subprogram itself to solve these pieces. This method of recursion is mathematical induction.

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Jennifer D’souza
Another example can be doing a good deed. When one person does a good deed it directly/indirectly inspires another person to perform a good deed.

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Nida Fathima.
Mathematical induction is generally used to prove that statements are true of all natural numbers. The usual approach is first to prove that the statement in question is true for the number 1, and then to prove that if the statement is true for one number, then it must also be true of the next number.
Intuitively, it’s proof by domino. First prove that you can tip over the first domino, and then prove that any one domino will tip over the next domino. If both those facts are certain, then you know for sure that all the dominoes will fall.
It’s particularly helpful when you need to prove something that’s not true or not meaningful for real numbers in general, such as confirming a formula for the sum of the first n natural numbers.

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Nashita : this concept is used in the game Dominos

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Roofiya-  Number of moves to solve the Towers of Hanoi puzzle.

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Andrea  example of falling dominoes. In a line of closely arranged dominoes, if the first domino falls, then all the dominoes will fall because if any one domino falls, it means that the next domino will fall, too.   A truly real-life example is the sinking of the Titanic: The crew of the Titanic realized that the ship was doomed when they realized that the bulkhead that was being flooded would be completely flooded, and that when a given bulkhead was completely flooded, the next bulkhead would undergo the same fate, thus sinking the whole ship.

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solution to the tower of Hanoi and other similar problems (see sources). Although there are several other proofs, induction is the most common and elegant of them all.

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Excellent girls !! Going good !! Leena Maa'm

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Trisheka

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zafreen

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1) fibonacci numbers     2) dominos    3)prime factorisation - Leha Mahesh Kumar

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Lakshmi Sunil. In causal inference inductive reasoning, you use inductive logic to draw a causal link between a premise and hypothesis. As an example: In the summer, there are ducks on our pond. Therefore, summer will bring ducks to our pond.

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Mawadda
Recursion

Recursion is a term that is used often in computer science. It is a method where the solution to a problem depends on solutions to smaller instances of the same problem. Recursion is mathematical induction.

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Hurairah Faatimah Muzammil

1) I'll start with the standard example of falling dominoes. In a line of closely arranged dominoes, if the first domino falls, then all the dominoes will fall because if any one domino falls, it means that the next domino will fall, too.

2) You are in line at Taco Bell. The first person in line orders a cheesy crunch. Also, if the person in front of you orders a cheesy crunch, you order it too, because it sounds so good. How many people in line order cheesy crunches? ;)

3) A truly real-life example is the sinking of the Titanic: The crew of the Titanic realized that the ship was doomed when they realized that the bulkhead that was being flooded would be completely flooded, and that when a given bulkhead was completely flooded, the next bulkhead would undergo the same fate, thus sinking the whole ship.

4) Electron transport

5) Electricity and osmosis