Why zero can't be divided by itself ?

2 Answers
May 30, 2018

It is indeterminate.

Explanation:

Because #a divide b# is asking the same question as what is #x# when:

#x times b = a#

with #0/0# you are asking what #x# makes this true:

#x times 0 =0#

The answer is any value of #x# no matter what so the answer is indeterminate, i.e. the solution cannot be determined which is different from undefined.

Other indeterminate forms would be #oo/oo#, #0^0#, #0 times oo#

May 30, 2018

I tried this:

Explanation:

Maybe it isn't a great explanation but...
Consider, for example, that you can evaluate it and get a result:

#0/0="result"#

where, resut is a number, say, #n#.

we get:

#0/0=n#

and from algebra taking the zero in the denominator to the right:

#0=n*0#

and so:

#0=0# which is true!

but ....it is true reagardless of the value of #n# (it always works!!!).

So, if they ask "what is the result of #0/0#" you will be forced to answer "all the numbers" that it is a bit like to say that you cannot have one result!