i stumbled across this thread through a google search of something entirely different. after reading some of the arguments here trying to explain to this poor kid why 0/0 is undefinable and cannot be used in math, i had to join the website just to try and help! lol
i think everyone is looking too much into this. basically he just wants to know why you cant divide by zero (at least that's what i'm getting out of it).
so let me put it to you as simply as i can so that you may understand this conundrum conceptually (and i say "conceptually" only because truly mathematically proving 0/0 as being undefinable is quite a bit more complicated. yet you can still have a conceptual understanding and be well on your way)
first of all, any number divided by itself is 1 (that's an axiom - it is true and inarguable)
1/1=1, 2/2=1, 3/3=1, so on and so forth
so then by HIS logic, if hypothetically we are able to divide by 0, then 0/0 would also equal 1
hmm... obviously there is a problem here. because 0/0 does NOT equal 1.
in fact 0/0 doesn't equal 0 either as u might otherwise be likely to surmise. it is just... nothing.
this is because in affect, what you are saying is that you have "0 0's" or in other words "no nothings". which is again... NOTHING. it doesn't exist! it is nowhere to be found. it is thus UNDEFINABLE. in fact anything over nothing is undefinable. this is because (now really pay attention here) YOU CANNOT HAVE A QUANTITATIVE AMOUNT OF NOTHINGS.
so that's it and it really is just as simple as that. pretty much that last statement sums things up about as consisely as i can possibly think of.
before i finish, i think it is also important to note here that (**warning - spoiler alert**) dividing by 0 is NOT the only thing that is undefinable in math. it is not like some unique case or something. for instance, did you know you also can't take the square root of a negative number (ha! bet that one will really get your head spinning lol). there are lots of things that are undefinable, because they simply dont work. they don't make any logical sense and that is essentially what math is all about. logic.
you can't blame the kid though for asking the question. it's an interesting problem that can be hard to wrap your head around just like with most concepts in math (even the basic ones!). at some
point in the past though, SOMEBODY had to ask this very question (and of course consequently figure it out). otherwise we wouldn't know what we do today. so i say, ASK ON!!!
if you would like to read on, i can explain further to you why your equations and assumptions are wrong. but hopefully i have shown you now that 0/0 or anything over zero is undefinable.
so first you assume that 0/0=x
what you are doing here is trying to solve for x. so you are saying that x must be some definable number. but we have already shown that 0/0 is UN-definable so right out of the gate the whole thing has effectively imploded in on itself.
HOWEVER, let's just play along here...
so next you say then that 0 must equal 0*x, and therefore 0=0
well, the problem here is that now you have just removed the varible you were trying to solve for in the first place from the equation. of course 0 multiplied by anything is indeed zero. but now that you have removed your variable from the eqation all you are saying is that 0=0 and x is no longer part of the equation. it has just become... nothing - hey there's that word again. it seems to come up alot when talking about dividing by 0
moving onward...
you then define x to be 5 while using your same equation and come to the conclusion that 0=0.
nothing wrong here! HOWEVER, we have already shown that all you are doing in the end is removing the variable and saying 0=0. but you haven't actually done anything.
now let's talk about the whole 0/x=0 thing (first of all you didnt really need to do any math to arrive at this, you could have just started here).
so you argue that since x can equal anything we want, why not make it 0 and thus 0/0=0. again we have already shown that this isn't true and in fact your argument that x can be anything while acting as the denominator is not entirely correct either. the denominator can be anything EXCEPT 0 for the very reason that it is undefinable (that's a real honest-to-goodness definition of denominators by the way. not something i made up). in fact later on in math when you are trying to solve very complex equations, if you ever arrive at 0 in the denominator, then you have reached a dead end. its a sign that you did something wrong and have to start over.
so now lets have a look at your last statement (and i'll quote you just to make sure i get it correct)...
"if you fallowed [followed] so far and remember that x can be any number[,] then that means zero can also be any and every number. So 0 can now equal 5 or any other number."
ok. i'm sorry, but i'm gonna have to be rash here. this is complete and utter nosensical gibberish. if YOU have been following so far, then perhaps you are starting to see why
I'll be happy to explain anyway...
i think you are missing a very fundamental alegbraic concept here. x CAN equal anything because it is simply a place holder. it doesn't have any value until you put it in an equation and say that it is equal to something - it is just something you are trying to solve for. merely a symbol for a place holder. 0 on the other hand is just.... 0. just like 1 is 1, 2 is 2 and so on.
let me illustrate my point...
let's say that 2x=6
now solve for x.
obviously we divide both sides by 2 to get (2x)/2=6/2 >> x=3
so in this instance, this example, this specific equation, x is 3. but it does not mean that x is ALWAYS 3. it was just a place holder for us to solve for.
well, that's it. i hoped this helped. although i didn't even notice how long ago this thread was started. perhaps by now you are a distinguished graduate math student working on your thesis about how 0/0 IS possible
i think everyone is looking too much into this. basically he just wants to know why you cant divide by zero (at least that's what i'm getting out of it).
so let me put it to you as simply as i can so that you may understand this conundrum conceptually (and i say "conceptually" only because truly mathematically proving 0/0 as being undefinable is quite a bit more complicated. yet you can still have a conceptual understanding and be well on your way)
first of all, any number divided by itself is 1 (that's an axiom - it is true and inarguable)
1/1=1, 2/2=1, 3/3=1, so on and so forth
so then by HIS logic, if hypothetically we are able to divide by 0, then 0/0 would also equal 1
hmm... obviously there is a problem here. because 0/0 does NOT equal 1.
in fact 0/0 doesn't equal 0 either as u might otherwise be likely to surmise. it is just... nothing.
this is because in affect, what you are saying is that you have "0 0's" or in other words "no nothings". which is again... NOTHING. it doesn't exist! it is nowhere to be found. it is thus UNDEFINABLE. in fact anything over nothing is undefinable. this is because (now really pay attention here) YOU CANNOT HAVE A QUANTITATIVE AMOUNT OF NOTHINGS.
so that's it and it really is just as simple as that. pretty much that last statement sums things up about as consisely as i can possibly think of.
before i finish, i think it is also important to note here that (**warning - spoiler alert**) dividing by 0 is NOT the only thing that is undefinable in math. it is not like some unique case or something. for instance, did you know you also can't take the square root of a negative number (ha! bet that one will really get your head spinning lol). there are lots of things that are undefinable, because they simply dont work. they don't make any logical sense and that is essentially what math is all about. logic.
you can't blame the kid though for asking the question. it's an interesting problem that can be hard to wrap your head around just like with most concepts in math (even the basic ones!). at some
point in the past though, SOMEBODY had to ask this very question (and of course consequently figure it out). otherwise we wouldn't know what we do today. so i say, ASK ON!!!
if you would like to read on, i can explain further to you why your equations and assumptions are wrong. but hopefully i have shown you now that 0/0 or anything over zero is undefinable.
so first you assume that 0/0=x
what you are doing here is trying to solve for x. so you are saying that x must be some definable number. but we have already shown that 0/0 is UN-definable so right out of the gate the whole thing has effectively imploded in on itself.
HOWEVER, let's just play along here...
so next you say then that 0 must equal 0*x, and therefore 0=0
well, the problem here is that now you have just removed the varible you were trying to solve for in the first place from the equation. of course 0 multiplied by anything is indeed zero. but now that you have removed your variable from the eqation all you are saying is that 0=0 and x is no longer part of the equation. it has just become... nothing - hey there's that word again. it seems to come up alot when talking about dividing by 0
moving onward...
you then define x to be 5 while using your same equation and come to the conclusion that 0=0.
nothing wrong here! HOWEVER, we have already shown that all you are doing in the end is removing the variable and saying 0=0. but you haven't actually done anything.
now let's talk about the whole 0/x=0 thing (first of all you didnt really need to do any math to arrive at this, you could have just started here).
so you argue that since x can equal anything we want, why not make it 0 and thus 0/0=0. again we have already shown that this isn't true and in fact your argument that x can be anything while acting as the denominator is not entirely correct either. the denominator can be anything EXCEPT 0 for the very reason that it is undefinable (that's a real honest-to-goodness definition of denominators by the way. not something i made up). in fact later on in math when you are trying to solve very complex equations, if you ever arrive at 0 in the denominator, then you have reached a dead end. its a sign that you did something wrong and have to start over.
so now lets have a look at your last statement (and i'll quote you just to make sure i get it correct)...
"if you fallowed [followed] so far and remember that x can be any number[,] then that means zero can also be any and every number. So 0 can now equal 5 or any other number."
ok. i'm sorry, but i'm gonna have to be rash here. this is complete and utter nosensical gibberish. if YOU have been following so far, then perhaps you are starting to see why
I'll be happy to explain anyway...
i think you are missing a very fundamental alegbraic concept here. x CAN equal anything because it is simply a place holder. it doesn't have any value until you put it in an equation and say that it is equal to something - it is just something you are trying to solve for. merely a symbol for a place holder. 0 on the other hand is just.... 0. just like 1 is 1, 2 is 2 and so on.
let me illustrate my point...
let's say that 2x=6
now solve for x.
obviously we divide both sides by 2 to get (2x)/2=6/2 >> x=3
so in this instance, this example, this specific equation, x is 3. but it does not mean that x is ALWAYS 3. it was just a place holder for us to solve for.
well, that's it. i hoped this helped. although i didn't even notice how long ago this thread was started. perhaps by now you are a distinguished graduate math student working on your thesis about how 0/0 IS possible
