Is Zero Divisible by Zero and Four?

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Homework Help Overview

The discussion revolves around the concept of divisibility, specifically whether zero is divisible by zero and four. Participants are examining the definitions and implications of divisibility in this context.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the definition of divisibility and its application to the numbers zero and four. There is a focus on the uniqueness of the integer in the definition of divisibility, as well as concerns regarding division by zero.

Discussion Status

The discussion includes attempts to clarify the definition of divisibility and its implications. Some participants express uncertainty about the treatment of zero in these scenarios, while others affirm the uniqueness of the solution for the equation involving four.

Contextual Notes

There is a mention of a potential misunderstanding regarding the definition of divisibility, as well as the concern about division by zero. The original poster references their textbook, indicating reliance on that source for definitions.

cragar
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Homework Statement


determine which are true and false.
4|0 and 0|0

Homework Equations


a is divisble by b provided there is an integer c such that

bc=a

The Attempt at a Solution


on the first one 4|0
4x=0 , 0 would work for this.
and 0x=0 any integer would work for this but I am worried about division by zero
or something weird with zero , maybe I am overlooking this.
 
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No, 0 does not divide 0. You definition
"a is divisible by b provided there is an integer c such that bc=a"
is not completely correct. It should be
"a is divisible by b provided there is a unique integer c such that bc=a"
 
I wrote it how my book wrote it. Thanks for your response by the way . So meaning there is only one integer c such that bc=a
 
cragar said:
I wrote it how my book wrote it. Thanks for your response by the way . So meaning there is only one integer c such that bc=a

Yep, I think so. What are numbers are there such that 4x=0?:rolleyes:
 
so x=0
 
cragar said:
so x=0

Yes, like HallsofIvy said (one unique solution)
 
ok , thanks , just making sure.
 

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