Express through basic quantifiers on the given domain:

  • Thread starter albert1992
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Z means that for all integers y, y squared does not divide x. This includes all prime numbers, but also includes 1, which is an exception to the rule.
  • #1
albert1992
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Homework Statement


x is square free (not divisible by a perfect square) on Z


Homework Equations


Z meaning all integers.


The Attempt at a Solution


I did a similar problem earlier that asked for the expression for prime numbers on the Natural numbers domain. For that problem the product of a*b with a,b >1 never equaled a prime number. So for this problem I believe that all of the prime numbers are included in the square free I'm just not sure how to integrate this.
 
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  • #2
What's wrong with the obvious, "For all y in Z, y2 does not divide x"?
 
  • #3
I think it works but what about 1

1 squared does divide the square free 1
 

Related to Express through basic quantifiers on the given domain:

1. What is the purpose of expressing through basic quantifiers?

The purpose of expressing through basic quantifiers is to describe the quantity or amount of something in a specific domain or set. This allows for a more precise and clear understanding of the information being conveyed.

2. What are basic quantifiers?

Basic quantifiers are words or symbols used to indicate the quantity or amount of something. They are commonly used in mathematical and scientific contexts to express numerical values or relationships.

3. What is a domain in the context of expressing through basic quantifiers?

In this context, a domain refers to the specific set of objects or values that are being quantified. For example, in the statement "There are 10 apples in the basket," the domain would be the basket of apples.

4. What are some examples of basic quantifiers?

Some examples of basic quantifiers include "all," "some," "none," "every," "at least," "at most," "exactly," and mathematical symbols such as "=", "<", and ">".

5. How do basic quantifiers differ from other types of quantifiers?

Basic quantifiers are typically used to express quantities or amounts in a more general or universal sense, while other types of quantifiers may be more specific or conditional. For example, the basic quantifier "all" states that something applies to every object or element in a domain, while a conditional quantifier such as "if...then" only applies to certain conditions being met.

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