Is this dividing by zero

[Bletchleyite]

maybe the question is being asked wrongly
if its asking 0% interest added or subtracted the answer would off course be the origional amount

Yep, I wonder if the OP is thinking about the way on some calculators the multiply/divide buttons are used for percentage operations even if they aren't strictly that.

 

[bb21]

0 divided by 0% of what?

You don't need to define 0% of whatever it is. It can be whatever you want it to be.

The question is essentially 0 divided by 0. I see we have an interesting discussion going on here. Where are our pure mathematicians on the forum?

The starting point of my question? The reverse operation of the equation expressed above, so makes perfect sense, but as to the answer, funny that it is not 10.

 

[MotCO]

0/0 is an interesting question. Clearly any nonzero number divided by 0 is undefined/infinity depending who you ask. But zero...you could argue 0/0 is just 0.

10/10 = 1; 5/5=1; 2/2=1; 1/1=1. Why isn't 0/0 = 1?

 

[EM2]

10/10 = 1; 5/5=1; 2/2=1; 1/1=1. Why isn't 0/0 = 1?

Well, it's 'how many tens in ten, fives in five' etc. but how many zeros are in zero? Zero is nothing, so how much of anything is in nothing? But also, how much nothing is in nothing?

 

[Belperpete]

Well, it's 'how many tens in ten, fives in five' etc. but how many zeros are in zero? Zero is nothing, so how much of anything is in nothing? But also, how much nothing is in nothing?

Anything divided by zero is usually taken as infinity. Consider X/Y Regardless of whatever X happens to be, the smaller Y becomes, the larger the result becomes. The closer Y becomes to zero, the closer the result becomes to infinity, so the logical conclusion is that when Y reaches zero, the result must reach infinity.

The exception to this rule is 0/Y. Whatever the value of Y, the result is always zero. You can make Y smaller and smaller, but the result will still be zero. So the logical conclusion is that when Y reaches zero, the result will still be zero.

And then we get to negative numbers. Say when you divide 6 apples among 2 less than zero people.

 

[big all]

because off this thread perhaps ??
https://www.railforums.co.uk/threads/delay-repay-for-zero-fares-on-oyster.175447/

 

[nlogax]

Always liked this explanation. Not that you’ll necessarily be any clearer afterwards.

 

[A Challenge]

From the starting screen, that appears to be using ÷0 to prove that 1=0, which is why in pure mathematics whenever something would involve dividing by zero you need to exclude that answer, for example if it is ÷x+2 it would have to say x≠-2.

It also proves that 1÷0=∞ by saying:

1÷1=1
1÷0.1=10
1÷0.01=100
1÷0.001=1000
1÷0.0001=10000
∴ 1÷0=∞

This is logical, in my view, as as you decrease the amount you are dividing 1 by the answer increases at the same rate, so if you make it down to 0 then it is infinite, as you can divide a number by 10 (or any other number for that matter) for the rest of eternity without reaching zero, and you can times the other number by 10 (or, again, any other number) for eternity and never reach ∞.

I am a first year A Level Further Maths Student

 

[Howardh]

If I have ten pounds, and multiply it with (or divide by) nothing, I should still have ten pounds as I've done nothing to that number. Yet mathematically and in reality I end up with nothing
ie £10 x 0 = £0!!

 

[Howardh]

Well, it's 'how many tens in ten, fives in five' etc. but how many zeros are in zero? Zero is nothing, so how much of anything is in nothing? But also, how much nothing is in nothing?

Nothing must be infinate? If not, it doesn'r exist so why is there a number for it?

 

[A Challenge]

If you are sharing it something (x) between two people, the highest amount both can get while getting the same amount is (x÷2), with one person the maximum amount you can get is x, and if there is 0 people the maximum that each (no) person can get is ∞, remainder x, and you can write that as a fraction (x÷0). I'm not sure if the remainder thing makes mathematical sense.

 

[krus_aragon]

I'm a little late to the party, but I feel obliged to weigh in having been employed in the past as a maths teacher.

When asking what 0% of a value is, it's worth remembering what that '%' symbol is. It represents "per cent" , or "per hundred".* So for every hundred in the original value, you take a certain proportion.

One common algorithm for calculating a percentage of a value is to express the percentage as a fraction out of a hundred (e.g. 5% is equivalent to 5/100), and multiplying the value with that fraction.

There is a well-known issue with dividing by zero, which (depending on who you ask) is undefined, impossible, or irrelevant. This is only an issue when the divisor (number that we divide by) is zero, for reasons already discussed upthread. In the case of percentages expressed as a fraction, the divisor is the denominator of the fraction, which is always 100. And even in the particular case of 0/100 x something (simplified to 0 x something), we're multiplying by zero. Zero lots of something is evidently zero. ("Go to the shop and buy zero packets of mince pies for me, will you?" )

Even if our algorithm did lead us to try dividing a value by zero, that would mean that our algorithm couldn't give an appropriate result. That wouldn't neccessarily mean that there was a problem with the idea of percentages, just this particular method of calculating them.


*There's also a '‰' sign, "per mille", for representing a proportion out of a thousand.

 

[JamesRowden]

From the starting screen, that appears to be using ÷0 to prove that 1=0, which is why in pure mathematics whenever something would involve dividing by zero you need to exclude that answer, for example if it is ÷x+2 it would have to say x≠-2.

It also proves that 1÷0=∞ by saying:

1÷1=1
1÷0.1=10
1÷0.01=100
1÷0.001=1000
1÷0.0001=10000
∴ 1÷0=∞

This is logical, in my view, as as you decrease the amount you are dividing 1 by the answer increases at the same rate, so if you make it down to 0 then it is infinite, as you can divide a number by 10 (or any other number for that matter) for the rest of eternity without reaching zero, and you can times the other number by 10 (or, again, any other number) for eternity and never reach ∞.

I am a first year A Level Further Maths Student

Approach from negative numbers rather than positive numbers and 1/x tends to minus infinity as x tends to zero, meaning that 1/0 is as much infinity as it is minus infinity. So for 1/0 to be infinity, infinity must equal minus infinity. To me this, plus the fact that a value can be infinitely small while being greater than zero, shows that 1/0 does not equal infinity, and 1 divided infinity is not zero. Another example is that something can be infinitely improbable and possible. For example, a string of ideal balanced coin tosses (50/50) untill the result is a head (assuming that one could toss a coin a never ending number of times) is no guarantee of eventually getting a head since the probability of getting a head remains constant (in this ideal scenario) no matter how many tosses have already occured in the string.

 

[Busaholic]

The answer is 42 - it always is (except when it's 23.)

 

[big all]

i much prefer hitchhickers guide to the galaxy
i actually find a whole long thread about nothing well off little use its all semantics where most off the thread content is about exact and pedantic where as the actual situation would be connected to an actual value as
zero multiplied by zero added to zero plus zero percent serves no actual purpose
now not a problem in reallity but seems to lack purpose other than confuse and inform people that nothing equals nothing or on a good day a bit less or possibly a bit more

 

[krus_aragon]

i actually find a whole long thread about nothing well off little use

That description could match a lot of other threads as well!

 

[Busaholic]

That description could match a lot of other threads as well!

A person with whom I share both a name and a birthday put it well -'Much Ado About Nothing.'

 

[BRX]

A person with whom I share both a name and a birthday put it well -'Much Ado About Nothing.'

In that case, 'nothing' had some quite particular meaning(s)...

 

[DynamicSpirit]

10/10 = 1; 5/5=1; 2/2=1; 1/1=1. Why isn't 0/0 = 1?

I would say that 0/0 is undefined because it can literally be anything.

The way I think of it is this: In mathematics, when you encounter 0/0 in a problem, the situation is usually more subtle. In practice, what you usually mean is that you have some quantity x and you're dividing by some other quantity y, and it happens that in your problem, both x and y become extremely small (in mathematical parlance: When x and y both approach zero). And you want to know what happens to x/y when they become very small. So when you say 0/0 what you actually mean is limit (as x approaches 0, and y approaches 0) of x/y. There's probably some everyday example of this to make that clear but I can't think of one offhand, so I'll give a couple of mathematical examples instead:

1. Suppose y is always twice x. So y=2x, and lim (x, y->0) x/y = x/2x = 1/2. So in this case, 0/0 turns out to be 0.5.
2. Suppose x is always y squared. So lim (x, y->0) x/y = (y^2)/y = y. Since we've said that y is approaching zero, the answer is zero. So in this case, 0/0 turns out to be zero.
3. Suppose x is always sin (y). The x/y = sin(y)/y. And as y becomes small, sin y becomes almost the same as y, so x/y = y/y = 1. So in this case, 0/0 turns out to be 1.
4. The example you gave above of saying 10/10 then 5/5 then 2/2 then 1/1 is basically doing the same thing: Letting two numbers become smaller and smaller. But you're doing it for x = y, therefore x/y = 1, which is why you came to the conclusion that 0/0 = 1.

Even if you can't follow all the mathematical details of the last few sentences, you may be able to see where this is heading: I set up more and more examples that will make 0/0 equal whatever I want it to equal. You want 0/0 to equal 6? I can set up an example to do that. You want 0/0 to equal pi squared/sqrt(2)? I can set up an example to make 0/0 equal that as well.

That's why we say that 0/0 is undefined: Because there's no one right answer: Until you give more information about the actual problem you're trying to solve, you could make it equal whatever you want!