Is Zero Divisible by Zero and Four?

In summary, determining whether 4|0 and 0|0 are true or false involves finding an integer c such that bc=a, where a=4 and b=0 for the first statement, and a=0 and b=0 for the second statement. For the first statement, the integer c can be any number, but for the second statement, there is no unique integer c that satisfies the equation, making it false.
  • #1
cragar
2,552
3

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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  • #2
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"
 
  • #3
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
 
  • #4
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?:uhh:
 
  • #5
so x=0
 
  • #6
cragar said:
so x=0

Yes, like HallsofIvy said (one unique solution)
 
  • #7
ok , thanks , just making sure.
 

What is divisibility?

Divisibility is the property of being able to divide one number by another without any remainder. In other words, if a number is divisible by another number, it can be divided evenly with no leftover amount.

How do I determine if a number is divisible by another number?

To determine if a number is divisible by another number, you can use the division algorithm. Divide the first number by the second number and if there is no remainder, the first number is divisible by the second number. For example, 12 ÷ 3 = 4, so 12 is divisible by 3.

What are the rules for divisibility?

There are various rules for divisibility depending on the number you are trying to divide by. Some examples include: a number is divisible by 2 if its last digit is even, a number is divisible by 3 if the sum of its digits is divisible by 3, and a number is divisible by 5 if its last digit is 0 or 5.

Why is divisibility important?

Divisibility is important in many areas of mathematics, such as prime factorization, finding common factors, and simplifying fractions. It is also useful in everyday life, for example when dividing items evenly among a group of people.

How can I improve my understanding of divisibility?

To improve your understanding of divisibility, you can practice solving problems and using divisibility rules. You can also explore the relationship between divisibility and other mathematical concepts, such as factors and multiples. Additionally, seeking help from a teacher or tutor can also aid in understanding divisibility.

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