Why is Division by Zero Not Possible?

  • Context: High School 
  • Thread starter Thread starter Giulio B.
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Discussion Overview

The discussion revolves around the concept of division by zero, specifically why expressions like "3/0" are considered undefined. Participants explore the implications of division by zero in mathematical terms and through practical analogies.

Discussion Character

  • Conceptual clarification, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant questions why "3/0" is not equal to zero, expressing confusion over the difference between multiplication by zero and division by zero.
  • Another participant asserts that "3/0" is left undefined, challenging the notion that it could be considered as zero.
  • A third participant explains that division is defined as multiplication by the inverse, noting that the inverse of zero does not exist, leading to a contradiction if one attempts to define division by zero.
  • One participant uses a practical analogy, stating that it is impossible to divide three straws into zero groups, emphasizing the logical inconsistency of such a division.

Areas of Agreement / Disagreement

Participants express differing views on the nature of division by zero, with some providing mathematical reasoning while others offer practical examples. No consensus is reached regarding the implications of division by zero.

Contextual Notes

Participants rely on different interpretations of mathematical definitions and practical scenarios, leading to unresolved questions about the nature of division by zero.

Giulio B.
i'm a height school student and this is a stupid question:

why "3 x 0 = 0" and "3/0 = nothing"? should make 0 too.

it bothers me from years
 
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"3/0" is not 'nothing', it is left 'undefined'. Why should it be zero?
 
division by zero is undefined.

Division is defined as multiplying by the inverse. Say you write a/b = x, you actually mean a * b^(-1) = x, where b^(-1) is defined the be the unique number such that b * b^(-1) = 1 = b^(-1) * b.

However, 0^(-1) does not exist: suppose it did. Then, 0 * 0^(-1) = 1. But for any a, 0 * a = 0. Hence, we have an obvious contradiction.

Thus, saying a/0 = a * 0^(-1) = x is completely meaningless, since 0^(-1) does not exist.
 
you can't divide 3 staws into zero groups.
You could divide them into 1 group of 3, or 3 groups of 1, or others if you cut the straws into smaller pieces. No mater how small the pieces there will just be more and more groups.
 

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