- #1
abc
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why can't we divide 1 by 0 ?
can anyone prove iy mathmatically ?
thanx
regards
abc
can anyone prove iy mathmatically ?
thanx
regards
abc
Why Dividing 1 by 0 is Impossible?
- Context: High School
- Thread starter abc
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Discussion Overview
The discussion revolves around the question of why dividing by zero is considered impossible in mathematics. Participants explore various arguments and analogies to illustrate the concept, touching on both theoretical and conceptual aspects.
Discussion Character
- Exploratory
- Conceptual clarification
- Debate/contested
Main Points Raised
- One participant asks for a mathematical proof of why dividing 1 by 0 is impossible.
- Another participant presents an argument involving a hypothetical number k representing 1/0, leading to conflicting results that suggest dividing by zero is nonsensical.
- A participant shares an analogy involving coconuts and monkeys to illustrate the absurdity of dividing by zero, highlighting that the scenario becomes nonsensical when there are no recipients (monkeys) for the division.
- Some participants humorously challenge the analogy, questioning the relevance of monkeys in mathematical proofs.
Areas of Agreement / Disagreement
Participants express differing views on the validity of the arguments presented, particularly regarding the use of analogies and proofs. There is no consensus on a definitive explanation for why dividing by zero is impossible.
Contextual Notes
Some arguments rely on hypothetical scenarios and analogies, which may not fully capture the mathematical principles involved. The discussion includes playful elements that may detract from the seriousness of the topic.
Who May Find This Useful
Readers interested in foundational mathematical concepts, the nature of division, and the implications of undefined operations may find this discussion relevant.
- #2
Nexus[Free-DC]
- 37
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There's a number of reasons why dividing anything by zero is absurd, but here's a simple argument:
Suppose there was such a number as 1/0, call it k.
Now suppose we find 1/(0+0). This must be equal to k/2 since the denominator in the second fraction is twice the denominator of the first fraction. But 0+0=0 and so we find that k=k/2. Therefore k=0.
But now we have 1/k=k and so k is plus or minus 1, which is not zero.
The point is that dividing by zero generally gives you conflicting results, or else you can make it give you any result you want. Neither of which is particularly useful.
Suppose there was such a number as 1/0, call it k.
Now suppose we find 1/(0+0). This must be equal to k/2 since the denominator in the second fraction is twice the denominator of the first fraction. But 0+0=0 and so we find that k=k/2. Therefore k=0.
But now we have 1/k=k and so k is plus or minus 1, which is not zero.
The point is that dividing by zero generally gives you conflicting results, or else you can make it give you any result you want. Neither of which is particularly useful.
- #3
abc
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thank u very much Nexus[Free-DC] for wonderful explanation ...
regards
abc
regards
abc
- #4
Math Is Hard
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This is something a math teacher told me long ago about dividing by zero. I hope I remember it right. I thought it was clever.
Suppose you have a bunch of coconuts that you want to divide evenly to give
to a group of monkeys.
If you have 6 coconuts and 3 monkeys, how many does each monkey get?
6 coconuts divided by 3 monkeys = 2 coconuts for each monkey.
If you have 3 coconuts and 3 monkeys, how many does each monkey get?
3 coconuts divided by 3 monkeys = 1 coconut for each monkey.
If you have 0 coconuts and 3 monkeys, how many does each monkey get?
0 coconuts divided by 3 monkeys = 0 coconuts for each monkey.
but if you have 3 coconuts and 0 monkeys, how many does each monkey get?
It's now a nonsense question because there are no monkeys!
Suppose you have a bunch of coconuts that you want to divide evenly to give
to a group of monkeys.
If you have 6 coconuts and 3 monkeys, how many does each monkey get?
6 coconuts divided by 3 monkeys = 2 coconuts for each monkey.
If you have 3 coconuts and 3 monkeys, how many does each monkey get?
3 coconuts divided by 3 monkeys = 1 coconut for each monkey.
If you have 0 coconuts and 3 monkeys, how many does each monkey get?
0 coconuts divided by 3 monkeys = 0 coconuts for each monkey.
but if you have 3 coconuts and 0 monkeys, how many does each monkey get?
It's now a nonsense question because there are no monkeys!
- #5
Gza
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I'm going to have to disagree with your proof Mathishard. My disagreeance stems from the fact that monkeys don't eat coconuts. 
- #6
Math Is Hard
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I stand corrected! 
- #7
HallsofIvy
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That's why monkeys seldom appear in formal mathematical proofs!
- #8
Gokul43201
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Gza said:I'm going to have to disagree with your proof Mathishard. My disagreeance stems from the fact that monkeys don't eat coconuts.
But they do like to chuck them around...especially at the heads of human passersby. Who said anything about eating ?
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