Why can the denominator of a fraction equal zero? Mathematically speaking.
I never understood this meme.
>>7706941
*can't
>>7706941
if x * y = z, then x = y/z.
1*0 = 0.
2*0 = 0.
1*0 = 2*0.
So if you allow division by 0 to mean anything, you could just divide both sides by 0 and end up with 1 = 2. Hence, "undefined" - there is no unique way to assign a meaningful value to it.
>>7706941
you can not divide 1 thing into nothing. what doesn't make sense is not being about to divide 0 by 0.
>>7706941
What an amazing coincidence.
Three-four threads on this exact same issue in the last week alone.
Go bug somebody at redit or something.
Maybe imgur.
Al least come up with better bait.
>>7706948
>Fuck off
why? its a legitimate point.
>>7706941
It can, but only in the complex numbers.
N/0 = ∞
N/∞ = 0
Ln(0) = ∞
e^∞ = 0
>>7706946
There's also this argument , heard it somewhere, it's cheese, but do its job
For exemple, take 1 pizza and cut in 2 parts, you get half a pizza, cut in 4 parts, you get a quarter of pizza.
Now cut it in 1/2 parts, you get 2 pizzas, cut it in 1/4 parts, you get 4 pizzas, as the number of parts you cut aproaches 0, the number of pizzas you get aproach infinity, thus a number divided by 0 is undefined
>>7706955
>why? its a legitimate point.
That's not exactly wrong.
If you think of fractions as ratios, 0:0 is a valid ratio.
Then again 0:anything is the same ratio, so it's kind of moot.
>>7706971
>It can, but only in the complex numbers.
Actually, the complex number system does not define division by 0, nor does it define arithmetic operations on ∞.
The name of the number system that defines this is called the "extended real number system".
https://en.wikipedia.org/wiki/Extended_real_number_line
>>7706941
The reason is because it creates a problem in algebra.
Take the following true equation:
1 * 0 = 2 * 0
Now divide both sides by 0:
1 * 0 / 0 = 2 * 0 / 0
And finally cancel out the 0s algebraically:
1 = 2
The result is a false statement. If you can start with a true statement and perform algebra on it to yield a false statement, then your algebra system is not very useful. To keep algebra useful, mathematicians insist on avoiding division by 0.
Why does my calculator say it's infinity??
>>7706973
if assigning infinity to it made sense in every context it would be acceptable
but it isn't
what happens if you divide a pizza into -1/2 parts? then -1/4? etc. until you arrive at negative infinity
1/0 has two possible values then infinity and -infinity which is obvious nonsense
>>7707005
shitty calculator
>>7706981
>https://en.wikipedia.org/wiki/Extended_real_number_line
Why isn't this used in place of the standard reals?
>>7706973
>1/0 has two possible values then infinity and -infinity which is obvious nonsense
Perhaps it's merely possible to approach infinity from both the positive and negative direction, just as you can get to zero from either the positive or negative side.
>>7706981
retard
https://en.wikipedia.org/wiki/Point_at_infinity
https://en.wikipedia.org/wiki/Riemann_sphere
>>7707099
Because you can't do all the ordinary arithmetic operations on the points at infinity.
>>7707103
That gets you the projective plane, which is a different beast altogether.
>>7706948
x / y = z implies that x = y * z
replace x with 3 and y with zero.
How many (z) zeros will it take to make a 3?
No matter if you have one, one hundred, one hundred thousand, or even infinite zeros - they will all add up to zero. You cannot make 3 (or any nonzero value) with any zeros no matter how many. Hence why 3/0 = undef.
0/0 is is also undefined but because of a different property; how many zeros does it take to make a zero? In this case, it's 0, 1, 2, etc. So all answers are valid, hence it's also undefined. You can see this behavior in various parts of mathematics.
>>7707099
> Why isn't this used in place of the standard reals?
Good question. I think that many mathematicians feel that the benefit you get is too small to justify the additional complexity.
In other words: Does it provide a new useful tool for solving problems? Or is it just an academic toy to play with?
>>7707107
You can't really on zero either
Can you divide nothing by nothing?
0/0
>>7707114
>Good question. I think that many mathematicians feel that the benefit you get is too small to justify the additional complexity.
>In other words: Does it provide a new useful tool for solving problems? Or is it just an academic toy to play with?
While I agree that it might not have particularly many uses, I always thought that the standard lacked symmetry which made it 'ugly'.
>>7707123
There is no definite answer because every possible number is an answer.
1*0=0
2*0=0
3*0=0
i*0=0
etc.
>>7707135
a * b = 0
2 * 0 = 0
2 = 0/2
FALSE
>>7707124
>the standard lacked symmetry
Could you elaborate? Sounds a bit like bulllshit
>>7707143
Well it doesn't have a multiplicative inverse, while every other number does.
>>7706941
No OP. No mean No!
In real numbers?
Real numbers form a field, and the field requires the existence of two separate entities 1 and 0 by definition which satisfy 1*x = x for all x in your field, and x + 0 = x for all x in your field (an easy consequence of this is 0*x = 0 for all x in your field).
Without the definition of a field, so if you just know about real numbers and intuition, well, here:
But if you could divide by 0, how would you meaningfully define it?
0 = 1*0
0 = 2*0
So, 1*0 = 2*0. If we can divide by 0, then we see that 1 = 2. But this is absurd because we know that 1 and 2 are different real numbers.
But we could repeat this argument for ANY real numbers instead of just 1 and 2.
So you can make anything equal anything if you can divide by zero. This is why we leave it undefined... because there is no useful or meaningful way to define it in real numbers.
>>7707189
>So, 1*0 = 2*0. If we can divide by 0, then we see that 1 = 2. But this is absurd because we know that 1 and 2 are different real numbers.
No that's 0/0 = 0/0;
Limits. The closest you get to zero, the closest you get to having a result approaching infinity. Both sides of 0 approach opposites in infinity.
If x approaches 0, then the division doesn't exist. If it approaches 0 "from the left" it approaches negative infinity. If it approaches 0 "from the right" then it approaches positive infinity.
It's pre-calc stuff.
>>7707196
No, it isn't.
That's a property of real numbers as I said.
for ALL real numbers x, 0*x = 0.
So if y is another real number different from x, 0*y = 0.
Since they are equal to the same thing, we can equate the two:
0*y = 0*x.
Now if the property x/x = 1 applied to all reals including zero, we would just divide both sides by 0 to get y = x. But this isn't true, because x and y were assumed to be distinct.
>>7706947
0 / 0 = x
0 = 0x
0=0
this is true for all x
thus 0 / 0 has infinitely many answers
compare to:
1/2 = x
1=2x
x=1/2
this is true for only one x
>>7707208
x * infinity = infinity
y * infinity = infinity
x * infinity = y * infinity
therefore y = x
>hurr durr der hur
>>7706941
Only Terryology can define x/0
>>7707160
But it does.
>>7707218
Infinity isn't a number and its also not an element of the real numbers what you said doesn't make sense. Don't be dumb. Apply yourself.
retarded thing from a guy who knows nothing about math, but what's stopping me from define 1/0 as a variable like i and working with it like we do with i?
you can divide it by 0, faggots.
>>7707310
>lol why cant invent math
>lol im edgy
ur retarded, mathematics is also discovered, u can do arithmetic with i, u define 1/0 as variable, you cant do arithmetic with it, it is useless
>>7707310
nothing. go try and see how tremendously useless it is
>>7707297
I meant for zero
>>7707320
Let's just set 1/0 = j, and say that j follows all of the traditional characteristics of a field. Voila. This shit isn't hard, cretins.
>>7707323
good point
>>7707360
whenever you do you end up with j hanging there and its value is indefinite.
>>7706941
"dividing" is actually multiplying by the inverse of the denominator. All numbers have an inverse, EXCEPT 0. The inverse of 0 is just undefined, so you cannot multiply by it. Hence, you cannot "divide" by zero.
>>7706941
I always thought it just was the north pole, except when N = 0, in which case it is undefined.
>>7706941
because
[math] \lim _{x\to 0^-} \frac{1}{x} = -\infty [/math]
[math] \lim _{x\to 0^+} \frac{1}{x} = \infty [/math]
[math] \therefore \lim _{x\to 0} \frac{1}{x} DNE [/math]
>>7706955
No, it's not. Why doea it not apply to 1×0?
stupid, simple answer: The system has defined it as such. It's a construct. Granted a very coherent definition.
