Ok I'm getting annoyed with people saying 0/0 is infinite. Zero groups of nothing equals well nothing. Yes on a graph it is -infinite and +infinite because how would you graph nothing? Or people saying that anything times zero equals so 0/0 can't be true. Because 0/0= (0)(x)=0. Well explain this then. If 0x1=0 and 0x2=0 then does 1=2?
x*(1/x)=? as x approaches 0. From here it's important to note that 1/x as x approaches 0 = infinity. thus the equation becomes x*infinity=? as x approaches 0
Quite true, but that is a solvable case:
Let, f(x)= x*(1/x) As, x-->0, the limit of f(x) approaches 1.
Division by zero
As for division by zero that is an indeterminate case. Additionally, zero has infinitely many factors.
If 0x1=0 and 0x2=0 then does 1=2?
This is a bit hard for me to word but...
Note that both equations are equivalent. Thus, 0*1=0*2=0 but it does not imply 1 != 2, since such factorisation cannot be performed on zero.
0 can be treated as infinite yes. Infinity is the highest number possible. 0 by any number is 0 so in this sense it's treated as infinite (the highest number possible).
Well, infinity is the highest number impossible. ; )
I've never heard anyone refer to 0 as being infinite.
Wait, everyone here is aware that 1 = 0.999..., right?
Look, the way multiplication works is that in xy you have x groups of y. If you have 0 groups you have 0. That is called logic. It means that however many groups of nothing you have it is still nothing. It doesn't mean if 1x0=0 and 2x0=0 then 1=2 because they are different numbers but it just doesn't matter when dividing by zero.
And dividing anything by 0 is infinite because there is an infinite amount of nothing in anything. I think though that because there is nothing in nothing 0/0=0.
But please don't ask this kind of question unless you understand how maths works because you clearly do not understand which makes your questions kind of stupid.
Dividing anything by zero is undefined, not infinity. If I had 5 cookies, and I split them up into 0 groups, then I could not have 5 cookies if there were no groups. On the other hand, if it is infinit, than I will be very happy dividing my chocolate-peanut butter cookies by 0.
i've only seen certain models use "any number excluding zero" / 0 as being infinity... i've yet to see it used as 0/0 as infinity in a class room... i've only ever seen a pure math course use it as indeterminate... or no solution.
You know, one of the classical problems of dealing with 0 is that we use it to define other sets - or at least we have in the past (some systems don't do this, but I don't know much about these systems). So by giving a definition of 0 (perhaps as the empty set, or using the identity function) we can then define the successor function (plus '+' to independently derive other sets (numbers). This gets complicated when we try to define more sophisticated function, like multiplication and division. But this reason alone isn't enough for us to not "trust math." There may, however, be good reason to view math for what it is - an accepted logical system that can take certain inputs and give appropriate outputs. But of course any arithmetical system we have is also incomplete: there will be statements in that system that are not provable within the system. This is an extremely problematic result on the meta-level, but I don't think it's enough to reject arithmetic.
Isn't infinity also undefined? As far as I can tell we are all correct. 0/0 is indeterminate, it is undefined, and it is infinite.
Infinity is defined as a number that permanently increases. It is not undefined. Undefined is a nonexistant or indeterminable number.
0/0 is undefined.
Technically, any real number divided by zero is undefined. You can't divide by zero.
Infinity is a concept used for limits. The limit of a positive number being divided by an approaching-zero number IS infinity. In fact, by L'Hopital's rule we can often find the limit of two divided numbers that are approaching zero, and it can be a finite number. But in any case, limits aren't real numbers, so really this paragraph is just a random math discussion I guess :P
Sorry for the double post but I wanted to add a proof.
If 1/3 is congruent to .3 repeating, and 1/3+1/3+1/3=1, then .3 repeating plus .3 repeating plus .3 repeating must also equal one. Also, find a number between .9 repeating and 1...I'll give you a hint, there isn't one.
Sorry for the double post but I wanted to add a proof.
If 1/3 is congruent to .3 repeating, and 1/3+1/3+1/3=1, then .3 repeating plus .3 repeating plus .3 repeating must also equal one. Also, find a number between .9 repeating and 1...I'll give you a hint, there isn't one.
