Explanation Definition: For a letter game with three undefined terms, the letters M , I and U and one definition which defines x as any string of I ’s and U ’s, the four axioms defined are: 1. Addition rule – For a string of letters ending in I , letter U may be added at the end. 2. Doubling rule – If there is Mx , then x may be added to get Mxx . 3. Substitution rule – If there are three I ’s ( III ), then this string can be replaced by U . 4 . Deletion rule – If UU occurs, it is dropped. Proof: Consider the given string of letters MI . It has to be proved that it is equivalent to MIUIU . Use doubling rule and add a I at the end of MI. M I → M I I Again use doubling rule and add a I at the end of MI. M I I → M I I I Again use doubling rule and add a I at the end of MIII

Nature of Mathematics (MindTap Course List)

13th Edition

ISBN: 9781133947257

Author: karl J. smith

Publisher: Cengage Learning

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Chapter 3.5, Problem 11PS

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To prove:

The theorem if given MI, then it can be equivalent to MIUIU in the letter game with three undefined terms of letters M,I and U and one definition “x meaning string of I’s and U’s”.

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Chapter 3.5, Problem 10PS

Chapter 3.5, Problem 12PS

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Nature of Mathematics (MindTap Course List)

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To prove: The theorem if given MI , then it can be equivalent to MIUIU in the letter game with three undefined terms of letters M , I and U and one definition “ x meaning string of I ’s and U ’s”.

Solution Summary: The author explains the sequence of steps to prove the theorem that if given MI, it is equivalent to MIUIU in the letter game with three undefined terms of letters M, I and U.

Videos

To prove:

The theorem if given MI, then it can be equivalent to MIUIU in the letter game with three undefined terms of letters M,I and U and one definition “x meaning string of I’s and U’s”.

Want to see the full answer?

Chapter 3 Solutions

To prove: The theorem if given MI , then it can be equivalent to MIUIU in the letter game with three undefined terms of letters M , I and U and one definition “ x meaning string of I ’s and U ’s”.

Solution Summary: The author explains the sequence of steps to prove the theorem that if given MI, it is equivalent to MIUIU in the letter game with three undefined terms of letters M, I and U.

Videos

To prove: The theorem if given MI, then it can be equivalent to MIUIU in the letter game with three undefined terms of letters M,I and U and one definition “x meaning string of I’s and U’s”.

Want to see the full answer?

Chapter 3 Solutions

To prove:

The theorem if given MI, then it can be equivalent to MIUIU in the letter game with three undefined terms of letters M,I and U and one definition “x meaning string of I’s and U’s”.