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Why Division by Zero is Undefined
publish date: 2026/05/23 08:46:47.585394 UTC
volume_mutePlease drag and drop the options to sort them
Sort the following logical steps in the correct order to show why division by zero leads to a contradiction.
Conclude all different numbers are equal — an absurd result
Assume division by zero is permitted
Observe that \(0 \cdot x = 0\) is satisfied by every number \(x\)
Division must yield a unique result, but \(0/0\) does not
Correct Answer
(1) Assume division by zero is permitted
(2) Observe that \(0 \cdot x = 0\) is satisfied by every number \(x\)
(3) Conclude all different numbers are equal — an absurd result
(4) Division must yield a unique result, but \(0/0\) does not
Explanation
The logical chain is: (1) Assume division by zero is allowed. (2) Then \(0/0\) requires \(0 \cdot x = 0\), true for all \(x\). (3) This implies all numbers are equal — a contradiction. (4) Since division must yield a unique result and this fails, division by zero is not permitted.
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012