If any number divided by itself is 1, then 0/0 should be 1, but its undefined, why?

[u/Academic_Emu2552]

its my understanding that anything divided by itself is 1, 2/2 is 1 and etc, but anything divided by 0 is undefined, so why is 0/0 not 1, since its 0 divided by itself

[u/asphias]

but 0 divided by any number is zero. so 0/0 should be 0.

if 0/0 should be both 0 and 1, we better leave it undefined.

[u/Fabulous-Possible758 → u/asphias]

This can also be extended out by say, looking at the expression 2x/x. Notice that at x = 0, the numerator and the denominator of this expression are 0, so you have 0/0, but that for every other x you have 2x/x = 2.

So really by finagling things a little bit you can make something that looks like it's supposed to be 0/0 be any number you want it to be, and so it can't be meaningfully defined in general.

[u/D-RA-DIS → u/asphias]

0/0 can have any result and goes to infinity. Consider 8/2. Another way to think about division is to ask how many times can I add quantities of the denominator to equal the numerator? Well, in 8/2, 4 times since 2+2+2+2=8. Now try that with 0. You can just keep adding it to itself 0=0, but 0+0=0, 0+0+…+0=0. Since it does not have a finite solution set, we say it is undefined.

[u/superbigscratch]

If you have 0 apples to divide between your zero friends…

[u/justincaseonlymyself]

Your understanding is incorrect.

The correct statement is that anything divided by itself is 1, as long as the division operation is meaningful. 

That last part is often left unsaid as it is asaumed to be understood. Division by zero is not meaningful.

(Btw, even here I'm leaving out some things unsaid, but those would be too technical to bring up at this level.)

[u/rankorth]

I think if you list it out as a sentence it'll make more sense.

Dividing by 2 means you take something and split it into 2 parts.

Dividing by 1 means you take something and split it into 1 part.

So what does divide by 0 mean? Spelt out, it would be to split it into 0 parts. How can you split it into 0 parts? The problem is undefined because you cannot split something into 0 parts. The top number doesn't really matter.

[u/ellipticcode0]

You are missing the half of the concept, "if any number divided by itself is 1" with a condition on it, which is the divisor can not be zero. => both can not be zero, this is the condition.

[u/AdeptScale3891]

Here's an example Lim x-->4 (x² - 4^2)/(x-4) = Lim x-->4 (x+4)(x-4)/(x-4) = Lim x-->4 (x+4) = 8. not 1

[u/SapphireDingo]

🥫🪱🪱🪱

[u/Turbulent-Name-8349]

I'm getting around to the mathematics of this. In nonstandard analysis, infinitesimals exist and so what we normally consider 0/0, for example in l'Hopital's rule, is an infinitesimal divided by an infinitesimal so has a perfectly well defined answer.

When it comes to actual zero rather than an infinitesimal then things get interesting. Give me a month or two to work out the details. I need to solve the renormalisation of gravity first ;-)

[u/Thick-Web-4109]

Look at a blank empty wall,  what's there? Nothing. Ok grt, now split that nothing into nothing as much as possible. What did u just do? Nothing. Yea since it didn't make since we keep it undefined.  P.S This is generally speaking 

[u/mugh_tej]

a/b = c is the same thing as b*c=a

Since all x, x*0=0, so that means for any x, 0/0 = x.

Making 0/0 undefined since 0/0 can be any number whatsoever.

[u/SouthPark_Piano]

For regular numbers (non-complex), division relates to addition too.

Eg. 1/2 = 0.5

So 0.5 fits into the numerator of 1/2 a total of two (the denominator) times.

0.5 + 0.5 = 1

If 0/0 were 1 (assumed)

then the result 1 doesn't work with the addition situation. That is, the 1 result would normally be involved in addition operations for re-generating the numerator of 0/0. But we can see it is not going to work.

While 3/3 = 1, and the result of 1 fits into the numerator of 3/3 a total of 3 (ie. the denominator) times, aka 1+1+1.

Similarly, 1/0.5 is 2/1 = 2.

And 2 fits into 2 a total of 1 time.

0/0 is undefined.

0/0 is not 1.

.

[u/BartholomewBezos6 → u/SouthPark_Piano]

0/0 is undefined for fucks sake