Why can’t I divide by zero?

The explanation of why we cannot divide any number by zero is really easy. The three links contain different explanations, but eventually, they all come down to one. To begin, it is said that we students are told that a division by zero is undefined. And this, supposedly is not entirely true, but somewhat true, they tell us this because they, and we eventually cannot define an answer that would work. But in the other hand, if we are told that a division by zero equals to infinity, then that is entirely NOT true. Why? Because as the contents say, infinity is not a number, it is simply like a concept let’s say, because if it would be a number, there would be many contradictions, like the “collision” of our whole number system.

So, as mathematician Mahavira (9th century A.D.) said “A number remains unchanged when divided by zero.”, we can get to the simple and easy conclusion that a number cannot be divided by zero simply because, if you multiply that number by zero, the answer will ALWAYS be zero.

Now, in the case of 0/0=0, we may say that that is true because 0x0=0, and that may lead to us thinking or realizing that dividing by zero can give you a real number, but this is wrong. We must not confuse, as I said above, any number times zero will equal zero, so therefore the answer to 0/0 can be any number. And also, we must not forget that any number divided by that same number, will equal to one (1/1=1, 2/2=1,3/3=1..), so in that case of zero, 0/0 is definitely not 1.

Examples • 3x5=15. That is correct. Now let’s see what happens with zero. 0x5=0, 0x50=0 or 0x50000=0, and with that we can clearly see that any number by zero will equal to zero.

• 10/2=5. Now when we multiply the answer times de denominator, it will give us the numerator of the division: 5x2=10. So this applies to the same rule of the previous example of when we multiply any number times 0 the answer will be 0.

• 0/0= undefined. The answer is undefined because instead of saying that it is undefined we would say that it is infinity, but let’s not forget that infinity is not a number.

Relationship between Rational Functions and the Division by Zero

What is a rational function? A rational function is any which can be written as the ratio of two polynomial functions. It is formed when a polynomial is divided by another polynomial.
Rational functions are written this way: f(x)= p(x)/q(x). In the equation, the variables p and q are meant to be polynomial functions. So now, to see the relationship between these two topics, we know that rational functions are sometimes involved with divisions by zero when trying to get the x-intercept and y-intercepts of a function. When doing rational functions we need to get the vertical and horizontal asymptotes. This I the equation: f(x)=a^(n)/b^(m). Now, we now that we get the vertical asymptote with the denominator of the function. The domain of f is the set of all points x for which the denominator is NOT zero. Division by zero is undefined, so that a solution causing formal division by zero is not accepted. So, to get the vertical asymptote there is no division by zero included. Now to get the vertical asymptote, we need to compare the degrees of the numerator and the denominator, and distinguish which it is by following the rules of: if nm= No solution (No horizontal asymptote). So, on the other hand, to get the horizontal asymptote, there is indeed a division by zero included.

Examples

• x^2/0= undefined. The denominator is 0 so the equation is undefined meaning that it is NOT a rational function.

• y= 2^2+1/ 4x-8. Can you have a zero in the denominator of a fraction? No. So therefore if we set the denominator equal to zero and solve, we will get 2. So therefore our VA=2. Now let’s get the horizontal asymptote. The degree of the numerator is bigger than the one of the numerator, so following the rules mentioned above, this function doesn’t have a horizontal asymptote.