## View Poll Results: divide by 0

Voters
8. You may not vote on this poll
• possible

1 12.50%
• not possible

7 87.50%

1. is it possible to divide by 0 i was talking to my teachers and they said it was impossible to but i have also read that its under debate as to what it does any

ideas on the topic?  2.

3. Think about this: Can you divide an apple into zero parts without using the magic you learned at Hogwarts?  4. What you read about it being under debate is wrong. You cannot divide by 0. It is defined as undefined, at least in the naturals/rationals/reals/complex/etc numbers.

There are number systems where the multiplicative inverse of 0 is defined, but you lose other nice properties in the process, so you can't have both normal math operations and division by 0 in the same number system.  5. Originally Posted by hackmuffin
is it possible to divide by 0 i was talking to my teachers and they said it was impossible to but i have also read that its under debate as to what it does any

ideas on the topic?
There is no debate.

Division by zero has no meaning.

If your teacher says differently, then you need another teacher.  6. Undefined, as I recall.

I'm also wondering if there's some rational expression that approaches a finite number as the denominator approaches zero?? I can't think of anything off the top of my head, but does anyone know of one out there?  7. Originally Posted by jrmonroe
Undefined, as I recall.

I'm also wondering if there's some rational expression that approaches a finite number as the denominator approaches zero?? I can't think of anything off the top of my head, but does anyone know of one out there?
If you let the numerator also approach 0 then there are lots of them and the limit can be anything that you want. x/x is particularly simple.

However, this has NOTHING to do with division by zero.  8. Originally Posted by jrmonroe
Undefined, as I recall.

I'm also wondering if there's some rational expression that approaches a finite number as the denominator approaches zero?? I can't think of anything off the top of my head, but does anyone know of one out there?
If you let the numerator remain a positive constant, as the denominator approaches zero, the function approaches either infinity or negative infinity depending on which side you approach zero from (i.e. negative infinity if you approach zero from the negative numbers and infinity if you approach zero from the positive).

DrRocket suggests letting the numerator approach zero. You can find out what happens in that case by using L'Hopital's rule. There are plenty of cases like this that exist. Another example is , as x approaches zero, the function actually converges at 1. Again, L'Hopital's rule makes this obvious.  9. Originally Posted by TheDr.Spo
Think about this: Can you divide an apple into zero parts without using the magic you learned at Hogwarts?  10. Originally Posted by hackmuffin is it possible to divide by 0 i was talking to my teachers and they said it was impossible to but i have also read that its under debate as to what it does any

ideas on the topic?
Once only was I ever asked by a student of my maths classes, "why cant' you divide by zero?". This was unusual surprise for it was a student in his late teens/early twenties.

I think the reason for this is, you're introduced to division at an early school age.
Its natural to ask your teacher the question. "Sir why can't you divide by zero" [apologies for the sexual discrimination]

Sir, either doesn't know or he realises that his pupils are too immature to understand the reason why.
So you grow up with 'you can't divide by zero' as an absolute law (more powerful even than the law of gravity). Its hard-wired into your brain. Hence my surprise.

But I knew I could construct a proof which would be understandable to the whole class. So here it was: (First explain what I'm going to do and then do it)

The method of proof is 'indirect proof', also called 'proof by contradiction', or 'reductio ad absurdum' (meaning reduce it to an absurdity).

This a valid method in standard logic and is widely used in logic and mathematics.

You assume the opposite (negation) of the statement you're wishing to prove. You then show that this assumption leads to a contradiction (or absurd situation).

It follows using standard 2-valued logic that the assumption was false, and hence the original statement was true.

1. You can divide by 0 [ assumption]

2. Let x be variable standing for a real number (x is an arbitrary real number)

3. So x / 0 = r [ r is some real no., the set of reals is closed under division (inc. 0 by assumption), division represented by the symbol / ]

4. So x = r × 0 [simple algebraic transposition, × stands for multiplication ]

5. So x = 0 [ rhs: since any real number multiplied by 0 = 0, so r × 0 = 0 ]

Now here is the crux: There is a rule in predicate calculus called 'universal instantiation' which states that if you can
show that any arbitrary member (x) of a set has a property (P), then all members of x have property P.

6. So all real numbers are equal to 0.

At this point I could have stopped, with the absurdity, but I decided to push on into 'the real world':

I started counting out aloud how many people there were in the classroom. "0, 0, 0 .... there's no one here!"

"How many people outside? 0, 0, 0,.... there's no one outside!
0, 0, 0, ... there's no buildings in this college.
0, 0, 0, ... there's no towns in England.
0, 0, 0, ... there's no countries, there's no world.
0, 0, 0, ... there are no planets.
0, 0, 0, ... there are no stars, no galaxies, no universe!"

At that point I turned to the student who asked the original question and said "Is that absurd enough for you?"
[ Howls of laughter ]

Thus 'You cannot divide by zero!'  11. 0/1 is 0.

By law, anything times it's reciprocal is 1.

So 1/0 is undefined.

So what times zero is one? Nothing!

There's no number (at least not in the real number system), which multiplied by zero yields one.  12. 1/0.00000000000000000000000001 is going to be large.

1/0.00000000000000000000000000000000000001 is larger.

Yet, 1/0 is as mathematics states, not possible. According to everything close to "0", 1/0 should approach infinity. 1/infinity should approach "0".

0 x infinity = 1 ?

The most likely reason why no such equations are allowed is because mathematics likes to have physical proof for its equations. So, until someone can prove with actual demonstrable proof in reality the idea of 0 x infinity = 1, it won't be allowed, presumably.  13. Firstly i would like to tell you that 1/0 is not possible and it's value is undefined.  14. Originally Posted by theQuestIsNotOver 1/0.00000000000000000000000001 is going to be large.

1/0.00000000000000000000000000000000000001 is larger.

Yet, 1/0 is as mathematics states, not possible. According to everything close to "0", 1/0 should approach infinity. 1/infinity should approach "0".

0 x infinity = 1 ?

The most likely reason why no such equations are allowed is because mathematics likes to have physical proof for its equations. So, until someone can prove with actual demonstrable proof in reality the idea of 0 x infinity = 1, it won't be allowed, presumably.
0 x ∞ = 1???

0+0+0+0+0+0+0............ should still equal zero, inductively predictably. Unless 0 could be change to 0.000000000000000.........1 then that times ∞ is 1.

But that doesn't make sense much... Absolutely parallel lines a light year apart would be able to intersect at point ∞, which I guess is only true in Projective Geometry.

In a hypothetical space, there are an infinite number of 2 dimensional planes (0 height) that make up our 3 dimensional space (finite height).  15. Eonos can you explain it little bit in a better way ................I am not getting you what you want to say .So plz explain it .  16. Originally Posted by amit28it Eonos can you explain it little bit in a better way ................I am not getting you what you want to say .So plz explain it .
If 0 x ∞ = 1, then an infinite of nothing is something. Well that doesn't make sense, since 0+0+0+0+0+0+0+0+0+0... should still equal zero.

And "nothing" of ∞ is also something.

But in Projective Geometry, we have a projective plane, which is different from the familiar Euclidean plane. We add in "points at infinity" where parallel lines can intersect.

On a plane, parallel lines have zero difference in their slope, they have exactly the same slope, so they never intersect, except in the projective plane. Even though the differential slope is zero, over an infinite distance it has built up making the parallel lines eventually intersect, an example of 0 x ∞.

Also, some theoretical physicists believe that our 3 dimensional space is constructed out of an infinite number of 2 dimensional planes.

But the 2nd dimension has no height (ZERO height), but an infinite number of them gives a defined measurement, our 3d reality. This is hypothetical though and most probably not a true physical aspect of space, but it is an example of 0 x ∞.  17. divided by 0 is meaning less i mean if you divided a value with 0 its ans is infinity which is meaning less.it must be divide with 0 but ans is infinity.so you cant do it.else it will be use in mathematics so you remind it  Bookmarks
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