Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. using field axioms and order axioms prove the foll

Using field axioms and order axioms prove the following theorems (explain every step by referencing basic...

90.2K

Verified Solution

Question

Advance Math

Using field axioms and order axioms prove the following theorems(explain every step by referencing basic axioms)

(i) The sets R (real numbers), P (positive numbers) and [1,infinity) are all inductive

(ii) N (set of natural numbers) is inductive. In particular, 1is a natural number

(iii) If n is a natural number, then n >= 1

(iv) (The induction principle). If M is a subset of N (set ofnatural numbers) then M = N

The following definitions are given:

A subset S of R is called inductive, if 1 is an element of S andif x + 1 is an element of S whenever x is an element of S.

The intersection of all inductive sets if called the set ofnatural numbers and is denoted by N

Answer & Explanation Solved by verified expert
4.1 Ratings (770 Votes)
By the definition of Inductive given here I have proved thefour theorems Hope you    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Zin AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Q

After 3 months of endurance training John (who you may remember from Applied Essay 3 is not very...

Advance Math
Q

describe and discuss the musculoskeletal system and describe 5 terms associated with this musculoskeletal system

Medical Sciences
Q

make a meal plan for a all day for a male who is 48 year old,diabete...

Biology
Q

How can the evidence of both assimilation and the signs of ethnic identity, that support a pluralistic...

Psychology
Q

Based on the book, Harry Potter and the Sorcerer's Stone, describe what kind of place is...

Psychology
Q

A tennis court is being expanded to accommodate sitting stands The original space that measures...

Basic Math
Q

A cell phone carrier claims that 90% of customers are very satisfied with the servicethey...

Basic Math
Q

Periodic Inventory Using FIFO, LIFO, and Weighted Average Cost Methods The units of an item...

Accounting
Q

Complete the below table to calculate the trend percents for all components of comparative income...

Accounting
Q

7 01:14:10 Required: Select the data type to its appropriate data examples: categorical or numerical....

Accounting
Q

suppose the correlation between the return on a stock and the market is 75%. The...

Finance
Q

Blaine Corporation is considering replacing a technologically obsolete machine with a new state-of-the-art numerically controlled...

Accounting