Why is division by 0 undefined?

Question

So I'm relearning high school math for college and I found I was getting x/0=0 wrong. I see it explained as 1/0.1=10 etc.. is bigger and bigger while if you put a negative on the front of that is gets smaller and smaller. This is what I'm not understanding. Let me phrase it this way.. 1+1=2 1+2=3 1+3=undefined 1+4=5 Do you see what I mean? There IS a number between those two equations, it's 4. So why is it hard to understand that between 1/0.1=10 and -1/0.1=-10 is 0? I see on khan academy he says you could argue equally that it's infinity and that's well, dumb. You can't make something out of nothing but in mathematics you CAN turn something into nothing (1*0).

Let's say I'm wrong, why can we say that 1*0 is 0? Why is it rational for me to put 1 pizza into a nothing pile but it's irrational to say I divided 1 pizza into equal nothingness?

I know it's easy to play Socrates, but the current mathematics around this doesn't make sense.

Answer 1

Another perspective:

If you say 10 divided by 2, it means how many times must you add 2 to get 10. Hence, the common wording: How many time does 2 go into 10. For any real number divided by another will give a larger answer as the second number gets smaller.

Try 2 divided by 0.001..... the answer is 2,000

2 divided by 0.0001: 20,000

We can easily see that dividing by a very small number will give an answer that is very large. Sometimes we say that dividing by 0 gives an answer of "infinity". But this is ambiguous. For example 1/0 would not be expected to be the same as 1,000,000 divided by 0. Thus, it is more correct to simply say that it is undefined.

Answer 2

think of it this way, If I have anything once, or one time, then I have anything, If I have one apple 1 time, I have one apple. so 1 apple 1 times is 1 apple. but if I have 1 apple NO times, then i simply don't have an apple at all do I? so anything zero times is zero, i.e. it is anything because you've stipulated that it happened zero times, i.e. it never happened at all. so anything times zero equals nothing.

If you have 1 apple, and you divide it by 1, you still have one apple. if you divide it by 2, you have half an apple. but if you divide it by nothing, you have done nothing. that doesn't mean you have 1 apple since 1 apple divided by 1 = an apple, 1 apple divided by nothing cannot also equal 1 apple. In effect, dividing something by zero is undefined because by definition you have done nothing.

Since we know that any integer multiplied by zero, = zero, and any integer divided by 1 = the same integer, we are left with any integer being divided by nothing as an undefined situation, there is no number that can represent the solution. hope this helps, it's simply that numbers have a domain and dividing by zero is not defined in the domain. good luck with this, the wikipedia explanation is pretty dense.