Hello, I'm Zerodactyl. I believe that it is possible to divide by zero. The reason that it hasn't been proven is because people overlook all of their own concepts. There have been remarks such as that dividing one by each shrinking decimal makes the number bigger, so zero would have to be infinitely big. However, if you pass zero and divide by -1, the result will not be bigger, but smaller. If you divide by zero, the answer is zero. Another common opinion is that you can't divide something into no parts. This originates from the rule of biology that matter can't be created or destroyed. However, using the same concept, nothing else works either. The definition of division is to break something into equal parts, but then the parts are still there. One part must stay as the result, but the rest of the parts are put aside. The answer to the division is not the breaking, but the quantity of the part. When there are no parts, the quantity is zero.
It is still not mathematically possible, but that's the point. Math is separated into five divisions: Mathematically possible, mathematically true, logically possible, logically true, and non-existant. If you can't divide by zero, then it would be because matter can't be destroyed. This is the logically possible division. However, using the same concept, the rest of division is impossible because it also destroys matter. Multiplication can't exist because matter can't be created. Subtraction can't exist because it destroys matter. 1+1 is the same as multiplication, therefore self addition doesn't exist, which challenges the possibility of the rest of addition. Since math can't logically be possible, it is mathematically possible, and so is division by zero.
If you still claim it to be impossible, consider this. Division by zero is, algebraically, equal to null, or non-existent. However, in slope, a straight line up has a slope of null because it is equal to division by zero. Therefore, if division by zero doesn't exist, then the x-axis line doesn't exist either. Translation: there is no such thing as up. Since there is obviously such thing as up, then there is division by zero. Math must be both possible and true. Just as common math is mathematically possible and mathematically true, division by zero is mathematically possible and logically true.
You may be wondering something right now. There is a good chance that in response to that last statement, you said "What?" I shall explain. In slope form, a straight line up could be displayed as, for example, (5,2),(5,4). When written in slope form (y2-y1/x2-x1), y2=4, y1=2, x2=5, and x1=5. Once the symbols are substituted in, it looks like: 4-2/5-5. Subtract, and the result will be 2/0. The straight line up, therefore, is equal to division by zero, so if division by zero doesn't exist, then up doesn't exist either.
Division by zero is known as a paradox. A paradox is something that can't seem to happen, but can. It would be a paradox if something were mathematically possible, but not mathematically true. Possible is to be the equation, and true is the result of it. Logical would be physically true or possible, and math is not physically true or possible. Nothing exists in the division of logically possible, so the only combinations are mathematically possible and mathematically true, and mathematically possible and logically true. A paradox is mathematically possible and logically true. Division by zero is a paradox, so it is logically true. The logical answer is zero.