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A)Write a Python function product(a, b) that recursively computes an

A)Write a Python function product(a, b) that recursively computes an

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a)Write a Python function product(a, b) that recursively

computes and returns the value of a times b. Use only the

addition operator, and do not use any loops. You can

assume that both parameters are non-negative integers.

b)Use induction to prove that your algorithm from the

previous part is correct

Solution

Recursion has something to do with infinity. I know

recursion has something to do with infinity. I think I know

recursion has something to do with infinity. He is sure I

think I know recursion has something to do with infinity.

We doubt he is sure I think ... We think, we convinced you

now, that we can go on forever with this example of a

recursion from natural language. Recursion is not only a

fundamental feature of natural language, but of the human

cognitive capacity. Our way of thinking is based on

recursive thinking processes. Even with a very simple

grammar, like \"An English sentence contains a subject

and a predicate. A predicate contains a verb, an object and

a complement\", we can demonstrate the infinite

possibilities of the natural language. Stephen Pinker

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phrases it like this: \"With a few thousand nouns that can

fill the subject slot and a few thousand verbs that can fill

the predicate slot, one already has several million ways to

open a sentence. The possible combinations quickly

multiply out to unimaginably large numbers. Indeed, the

repertoire of sentences is theoretically infinite, because

the rules of language use a trick called recursion. A

recursive rule allows a phrase to contain an example of

itself, as in She thinks that he thinks that they think that he

knows and so on, ad infinitum. And if the number of

sentences is infinite, the number of possible thoughts and

intentions is infinite too, because virtually every sentence

expresses a different thought or intention.\"1

We have to stop our short excursion to recursion in

natural languages to come back to recursion in computer

science and finally to recursion in the programming

language Python.

The adjective \"recursive\" originates from the Latin verb

\"recurrere\", which means \"to run back\". And this is what

a recursive definition or a recursive function does: It is

\"running back\" or returning to itself. Most people who

have done some mathematics, computer science or read a

book about programming will have encountered the

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a)Write a Python function product(a, b) that recursively computes and returns the value of a times b. Use only the addition operator, and do not use any loops. You can assume that both parameters are non -negative integers. b)Use induction to prove that your algorithm from the previous part is correct Solution Recursion has something to do with infinity. I know recursion has something to do with infinity. I think I know recursion has something to do with infinity. He is sure I think I know recursion has something to do with infinity. We doubt he is sure I think ... We think, we convinced you now, that we can go on forever with this example of a recursion from natural language. Recursion is not only a fundamental feature of natural language, but o f the human cognitive capacity. Our way of thinking is based on recursive thinking processes. Even with a very simple grammar, like \"An English sentence contains a subject and a predicate. A predicate contains a verb, an object and a complement\", we can demonstrate the infinite possibilities of the natural language. Stephen Pinker phrases it like this: \"With a few thousand nouns that can fill the subject slot and a few thousand verbs that can fill the predicate slot, one already has several million ways to open a sentence. The possible combinations quickly multiply out to unimaginably large numbers. Indeed, the repertoire of sentences is theoretically infinite, because the rules of language use a trick called recursion. A recu ...
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