Can Division by 1 Really Be Considered Division?

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Discussion Overview

The discussion revolves around the concept of division by 1, exploring both mathematical and physical interpretations. Participants examine whether dividing by 1 can be considered a meaningful operation, using metaphors such as dividing a pie to illustrate their points. The conversation touches on the implications of language and the nature of mathematical operations.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants argue that dividing by 1 does not involve any actual division, as it results in the original quantity remaining unchanged.
  • Others suggest that this perspective is a matter of language and that the concept of division can have different meanings in different contexts.
  • A few participants mention that division by 1 can be viewed as a "do nothing" operation, similar to adding zero in addition.
  • There is a discussion about the limitations of using physical metaphors, such as dividing a pie, to represent mathematical operations, particularly when considering irrational numbers.
  • Some participants challenge the notion that dividing by 1 is trivial, suggesting it raises interesting questions about mathematical operations.
  • One participant introduces the idea that division by 0 is conceptually problematic, contrasting it with division by 1.
  • Several participants express confusion over the implications of their arguments, indicating a lack of clarity in the definitions and interpretations of division.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether dividing by 1 is meaningful or merely a linguistic construct. Multiple competing views remain, with some asserting it is a valid operation while others argue it lacks substance.

Contextual Notes

Participants highlight the potential for equivocation in the term "divide," noting that it can refer to both arithmetic operations and physical separation, which complicates the discussion.

Who May Find This Useful

This discussion may be of interest to those exploring the philosophical implications of mathematical operations, language in mathematics, or the conceptual understanding of division.

MrXow
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Oddly enough I came across this on Uncyclopedia.
Can you really divide by 1?
I know that it can be mathematically done with ease, but physically can it be done?
Imagine a pie, and your dividing tool is your knife. If you want to divide the pie in 2 you can do that just cut the pie down the middle. If you want to divide it by 4 just cut it down the middle then do it again perpendicular to the original cut. But if you want to divide by 1 you end up not using your knife at all. You therefore don't divide the pie and do not divide by 1.

I hope this is the right forum.
 
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By your same logic, you can only divide by integers.
 
MrXow said:
But if you want to divide by 1 you end up not using your knife at all. You therefore don't divide the pie and do not divide by 1.
I think this is merely a matter of language. Natural language has evolved to include an artificial distinction between "0" and "more than 0". (or more generally, between "less than 0", "0", "1", and "more than 1") While this is efficient for everyday communication, it has the unfortunate side-effect of constraining our thought -- we have a habit of excluding special cases when we really ought not to do so.


And another thing -- don't make a fallacy of equivocation. There are at least two distinct meanings for the word "divide" in your post: the English verb meaning a particular arithmetic calculation, and the English verb meaning to separate into parts. That they use the same word does not mean they are the same thing.
 
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MrXow said:
Oddly enough I came across this on Uncyclopedia.
Can you really divide by 1?
I know that it can be mathematically done with ease, but physically can it be done?
Imagine a pie, and your dividing tool is your knife. If you want to divide the pie in 2 you can do that just cut the pie down the middle. If you want to divide it by 4 just cut it down the middle then do it again perpendicular to the original cut. But if you want to divide by 1 you end up not using your knife at all. You therefore don't divide the pie and do not divide by 1.

I hope this is the right forum.

what do you get, when you want to divide a pie by 1? The entire pie itself.

what do you get when you want to divide a number by 1? The number itself.
 
nesna said:
what do you get, when you want to divide a pie by 1? The entire pie itself.

what do you get when you want to divide a number by 1? The number itself.

Yes so you don't actually divide the pie or the number. If you want to say oh I wonder what 7/1 is. You already have the answer before you divide. And your not even dividing it up.
 
MrXow said:
Yes so you don't actually divide the pie or the number. If you want to say oh I wonder what 7/1 is. You already have the answer before you divide. And your not even dividing it up.

You're confusing yourself. Of course dividing by 1 is possible. If it was impossible, you'd have no answer.
 
I mean its impossible because you don't actually do any dividing. The answer is already there and you do not divide it.
 
It's like a limit, sin(x)/x never gets to 0, but you know that it would be 1. You don't actually divide by 1 you just know that like 7/1.00000001 is roughly 7.

maybe that's a bad example.
 
MrXow said:
I mean its impossible because you don't actually do any dividing. The answer is already there and you do not divide it.

So you're saying it's a tautology? That still doesn't make dividing by 1 impossible.
 
  • #10
It's not a totally trivial observation. It's interesting that there exist certain mathematical operations which are equivalent to doing nothing at all. Maybe the OP is going to grow up to be a group theorist!
 
  • #11
For those of you still debating this you need to read this again:

Hurkyl said:
And another thing -- don't make a fallacy of equivocation. There are at least two distinct meanings for the word "divide" in your post: the English verb meaning a particular arithmetic calculation, and the English verb meaning to separate into parts. That they use the same word does not mean they are the same thing.
 
  • #12
Dividing by one is basicly the 'do nothing' operation from group theory. It is the same as the 'add zero' operation under addition. The denominator tells how many pieces are left of the whole after you use the knife on the pie. So division by 2 is 'make one slice across the pie and leave 2 pieces', division by three is 'make 2 slices with the knife and leave three pieces,' etc. It is easy to see that on this incremental basis division by 1 is 'make no slices with the knife and leave one whole piece.' This would also go towards explaining why division by 0 is impossible as it is -1 slices with the knife and the command would be 'take away a slice that does not exist made by the knife and make the entire pie disappear (0 pieces).'
 
  • #13
Ya the pie metaphor doesn't explain negative pie.
 
  • #14
Please not think your kindergarten maths has anything to do with the concept of division.
 
  • #15
christianjb said:
It's not a totally trivial observation. It's interesting that there exist certain mathematical operations which are equivalent to doing nothing at all. Maybe the OP is going to grow up to be a group theorist!

What's the OP?
 
  • #16
MrXow said:
What's the OP?

Original poster
 
  • #17
Is this topic over yet? If it is then I need someone to explain why I cannot add 0 to my pie... :biggrin:
 
  • #18
Now all we need to do is learn how to physically divide the pie by a half, and never go hungry again :)
 
  • #19
MrXow said:
What's the OP?

That's you. :)
 
  • #20
MrXow said:
It's like a limit, sin(x)/x never gets to 0, but you know that it would be 1. You don't actually divide by 1 you just know that like 7/1.00000001 is roughly 7.

maybe that's a bad example.

There are much better examples, especially since if x=pi then sin(x)/x is, in fact, equal to zero.
 
  • #21
MrXow said:
Oddly enough I came across this on Uncyclopedia.
Can you really divide by 1?
I know that it can be mathematically done with ease, but physically can it be done?
Imagine a pie, and your dividing tool is your knife. If you want to divide the pie in 2 you can do that just cut the pie down the middle. If you want to divide it by 4 just cut it down the middle then do it again perpendicular to the original cut. But if you want to divide by 1 you end up not using your knife at all. You therefore don't divide the pie and do not divide by 1.

I hope this is the right forum.

Division is a mathematical operation between numbers or functions of numbers.
Separating objects into parts is not division.

That we can simulate the operation of division applied to pies etc, has restrictive meaning.

What would (pie)/pi mean? I don't think there is a knife sharp enough to cut irrational numbers of parts, do you?

Applied mathematics tries to interpret mathematical operations into physical happenings, often without meaning, as you have described.
 
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  • #22
Hurkyl said:
And another thing -- don't make a fallacy of equivocation. There are at least two distinct meanings for the word "divide" in your post: the English verb meaning a particular arithmetic calculation, and the English verb meaning to separate into parts. That they use the same word does not mean they are the same thing.

That explains it perfectly. If it is still not clear...read it again and again and again...:biggrin:
 

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