 # Tetration Fixing a € R -{0}, consider the recursive functions ...

## Question

Tetration Fixing a € R -{0}, consider the recursive functions f,g : Z+ ->R defined as follows: f(1) = g(1) = a while f (n + 1) = aᶠ(ᶯ) and g(n + 1) = g(n)ᵃ
(a) Write out expressions for f(3) and g(3) in terms of a, and compute their values in case a = 10.
(b) Give a simplified expression for g(n), for an arbitrary n.
(c) What is the property that exponentiation lacks, a property that addition and multiplication enjoy, that is illustrated by the difference between f and g? As a remark, the function is called tetration.

Explain in your own words, making up a metaphor if you like, why induction is a valid method of proof of ɏnP(n), where P is some predicate on N.

## Solution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

Induction is a valid method of proof because this method checks the truthness of the statement at all values of n. Also, each truth value of the statement is based on the previous statement. For example for n =1, P(1) -->...

By purchasing this solution you'll be able to access the following files:
Solution.pdf and Solution.docx.

\$10.00
for this solution

or FREE if you
register a new account!

PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

### Find A Tutor

View available Discrete Math Tutors

Get College Homework Help.

Are you sure you don't want to upload any files?

Fast tutor response requires as much info as possible.