Is Zero Divided by Zero Equal to One?

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SUMMARY

The division of zero by itself is not equal to one because zero is not part of the multiplicative group, making the operation undefined. This concept is grounded in mainstream mathematics, as taught in basic school textbooks. Many individuals mistakenly believe that since any number divided by itself equals one, zero should follow the same rule; however, this leads to nonsensical results. The confusion surrounding this topic is common, but it is essential to understand that zero is indeed a number, yet its division by itself is not valid.

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  • Understanding of basic arithmetic operations
  • Familiarity with the concept of numbers and their classifications
  • Knowledge of mathematical definitions regarding division
  • Awareness of the properties of the multiplicative group
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  • Research the properties of the multiplicative group in mathematics
  • Study the definitions and implications of division by zero
  • Explore the concept of undefined operations in mathematics
  • Examine common misconceptions in basic arithmetic
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Students, educators, mathematicians, and anyone seeking clarity on the principles of arithmetic and the specific properties of zero in mathematical operations.

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Why is the division of zero by itself not equal to one,since it is conventional that any number divided by itself is equal to one?,or maybe is zero not a number?
 
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Dividing by zero is not defined. You can pretend it is defined and get nonsense results if you like. Zero is a number, yes. A lot of people are confused about this, you are not alone. Some people make up stuff about this problem. PF discusses mainstream Math, like you find in basic school textbooks, not personal theories.

We get this question frequently.

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Mbuso said:
Why is the division of zero by itself not equal to one?
Because zero isn't part of the multiplicative group. The question does not exist. It's as if we asked why we can't breath on the moon.
 

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