I wonder why one cannot in maths divide numbers with null. Example: why it is not possible to state 4/0 = 4 (4 is divided by 0 - in other words thus 4 is NOT devided and thus remains 4. (the only reason which I can think of (the reason that it is not possible to divide with null) is that you can arrive at a strange result by 0/0=1 (in the sense that 0 contains 0 or the number divided by itsef is 1) Is there any other explanation?
ProCop, Consider that in the equation y = 4/x, as a positive x approaches zero, y approaches infinity. At 4/0 you’d be “beyond infinity” (for lack of a better term) which doesn’t make sense. If you graph out the equation y = 4/x, you’ll see what I mean; you can’t plot 4/0.
If I understand you right, you are proposing that 0 does not really exist. (0 equals infinitely small number: number greater than 0)
Look, I'll prove to you that your theory isn't true, ProCop Divison does two things. It tells you how many times you can fit a number of a cetain size into another number and, if you devide a number into a certain number of peices, how big those peices are. So you are saying 1/0 = 1 But then 1/1 = 1 So you could claim that 1/1 = 1/0 And wind up with 1=0
Take another point of view x/y = z means the answer to y * z = x. If y = 0 then the answer to the later is not a single answer but is any number including infinity. From this point of view, the mistake is falsely assuming that x/0 has a single answer. A natural mistake because x devided by other numbers nearly always has a single answer.
<i>why it is not possible to state 4/0 = 4</i> Let's multiply both sides of that equation by zero. Then we get: 4/0 × 0 = 4 × 0 or 4 = 0 That is contradictory. So, what should the answer be? i.e. what is the value of x for 4/0 = x? Clearly, x cannot be any finite number. If x = infinity, then multiplying both sides by zero we get: 4 = infinity × 0 This seems ok, until you try something like 5/0, which gives: 5 = infinity × 0 = 4 or 5 = 4. The only solution to the problem is to say that any expression of the form x/0 is <b>indeterminant</b> or <b>undefined</b>. That avoids the contradictions.
The last few years, sportscasters have taken to describing a victorious team, say, in baseball, as having "doubled up" their opponent when the final score is 4-2, 6-3 etc. It's as if "doubling up" is a big deal. My contention is that if a team is beaten by a score of 1-0, why not say they were "infinitied up," since zero times infinity is zero! It certainly sounds more impressive to be "infinitied up" than merely being "doubled up." Actually, I say just give the damn score!
<B>The only solution to the problem is to say that any expression of the form x/0 is indeterminant or undefined. That avoids the contradictions.</b> OK. Really nice explanation. (But does it not mean that 0 is not fully/really a number?)
"OK. Really nice explanation. (But does it not mean that 0 is not fully/really a number?)" I guess you would have to say what YOU mean by a number! The way I use the word "number" saying "we cannot divide by 0" only means "we cannot divide by 0". It does NOT mean 0 is not a number! "But, what would an (ordered) field look like if we were to have x/0 = 1 ?" In any field (any ring, actually) 0*x= 0 so if x/0= 1 we would have to have x= 0*1= 0 for all x. That's one reason the definition of field includes "has more than one member". "Take another point of view x/y = z means the answer to y * z = x. If y = 0 then the answer to the later is not a single answer but is any number including infinity." No, that's not true. If x is not 0 then 0*z= x has NO answer. If x= 0 THEN 0*z= 0 has every number as answer. That's why we use the phrase "undefined" for x/0 with x not equal to 0 and "undetermined" for 0/0. By the way, infinity is NOT a standard real number. If you go around saying "x/0= infinity" without making it clear that you are just using infinity as a way of saying "does not exist" mathematicians will look at you funny. (Actually, if you go around saying "x/0= infinity" EVERYONE will look at you funny!)
What I meant by being a number is having the following qualities: - having precise value - mathemathical operations (multiplying, substracting, dividing etc)are applicable to it Actually, when thinking about this I am inclined to place 0 as being an artificial number, (existing only for the convenience of mathematicians) because the ultimate row of numbers never begins and never ends (there exists no highest and no lowest number - no place for 0 enywhere).
Indeterminate.<br> If you insist on writing down this expression and asking what it is, well, why not just use basic algebra to work it out: 0/0 = x now clear the fraction by multiplying by 0 0/0 * 0 = x* 0 0 = x*0 so x is...
RE:chroot <b>So the presence of an apple is natural, but the absence of an apple is artificial? </b> Let's have a look at the contains of my right trousers's pocket: The contains is class "natural": 1 tissue 3 keys class "artifficial": no money no gun no knife no condom( - I must remember that!!) no 99,99999% of the substantives of the Webster Dictionary How about that?
