Why Can't we Divide By 0

Is value X is divided by 0 is Possible ?

In the world of Mathematics. Many strange results are possible when we change rules . But one rule that most us have been warned not to Break don't divide by zero. How can the simple combination of an every number and a basic operations cause such problems . Normally divide by smaller and smaller number gives you the bigger and bigger answers.Ten divided by two is Five. Ten divided by one is Ten.Ten divided by one millionth is Ten millonth And so on.

It seems like if you divide by numbers that keep shrinking all the way to Zero that answer will go largest thing possible

Then isn't the answer to 10 divided by zero actually infinity ? It seems to plausible

But all we really is that if we divide 10 by a number that tends towards zero the answer tends towards infinity and that's not the same thing as the saying that 10 divided by zero is equal to infinity or value not defined

Division really means Ten divided by Two could mean how many times must we add two together to make 10 or 2 time what equal 10 ?

Dividing by a number is essentially the reverse of multiplying by it in the following way if we multiply any number by a given number X we can ask if there's a new number we can multiply by afterwards to get back where we started if there is new number is called the Multiplication Inverse of X

For example if we multiply three by two to get six you can multiply by one half to get back to three .So the Multiplicative Inverse of 2 is one half and multiplicative inverse of 10 is one tenth As we might notice the product of any number and its multiplicative Inverse is always 1 if we want to divide by 0 we need to its multiplicative inverse which should be 1 over 0 This would have to be such a number that multiplying it by 0 would give 1  But anything multiplied by 0 is still 0 such a Number is impossible So 0 has no multiplicative Inverse .

After all mathematicians broke the rule before for a long time there was no such thing as taking the square root of Negative Numbers But then mathematicians defined that square root of negative one as a new number called i opening up a whole new mathematical world of complex numbers. So if they can do that couldn't we just make up a new rule say that the symbol infinity means 1 over 0 .According to the rule of Multiplicative inverse of 0 times infinity must be equal to 1 

that means 0 times infinity plus 0 times infinity should equal 2 Now by the Distributive Property the left side of the equation can be rearranged to 0 + 0 times infinity since zero plus zero is definitely 0 that reduces down to 0 times infinity Unfortunately we have already defined this
As equal to 1 while other side of the equation is still telling us it's equal to 2. So 1 = 2  this is not necessarily wrong its not true in our normal world of numbers

 There's a still a way that can be mathematically valid if one two every other number  were equal to zero But having infinity equal to zero is ultimately not  all that useful to mathematician or anyone else.