Can Division by Zero Be Solved in Mathematics?

In summary, the conversation discusses the concept of divisions by zero in general math and differential equations. It explains that divisions by zero cannot be solved and attempting to do so can lead to contradictions and the creation of a new arithmetic. The conversation also touches on the idea of using personal theories and why they are not allowed on the platform.
  • #1
IDK10
67
3
First of all, I didn't know where to put this in general math or differential equations.

Let's start with the basic, x/0 = α. Where α is every number and decimal number from -∞ to +∞, by rearranging, we get x = 0α, x= 0, therefore only 0/0 = α. Now, we can integrate this with graphs.

Take the equations:
y=0/0,
and y=x/0, and the variant y=(x+a)/0

y=0/0:
If y=2 then there will be a horizontal line going through the points (x, 2), where x is any number on the x-axis. However, 0/0 = α, and therefore y=α, and as this means there will be infinite jorizontal lines, the entire graph will be full.

y=x/0:
Now we are dealing with a change in x. By rearrangin, we get x=0, therefore a graph of y=x/0 ≡ x=0. Another way of proving this, is that when x is greater than, or less than 0. It won't work, for example y=1/0, 0y=1, 0=1, but 0≠1, but if it is replaced with 0, y=0/0, we get the infinite vertical line from before, but is trapped at x=0 because of the change in x making other lines impossible.

y=(x+a)/0:
This time, by rearranging, we get x=-a. By using what we said before, it works the same way. For example, y=(x-4)/0. If x = 4, then we get y=0/0, therefore we get an infinite vertical line at x=4, but mot anyother line because if x/0=0 (where x≠0), it won't work.

The gradient of y=x/0:
y=x/0, is the same as y= x*1/0, and by differentiation we get dy/dx = 1/0, but 1/0 is impossible since, by rearranging, we get from 1/0=x to 1=0, but 1≠0, yet there is a gradient, otherwise it wouldn't be traveling upwards, the graphs and differentiation contradict each other.

The gradient of y=(x+a)/0 will be the same, as nothing would change to the line, apart from its translation across the x-axis. Proof:
y=(x+a)/0
x - dy/dx = 1
a - dy/dx = 0
dy/dx = (1+0)0 = 1/0.
 
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  • #2
IDK10 said:
First of all, I didn't know where to put this in general math or differential equations.

State what you are trying to do. "Solved divisions by zero" doesn't say anything specific.
 
  • #3
IDK10 said:
"I solved divisions by zero": First of all,
... there is no problem to solve. ##0## when it is used alongside addition and multiplication, denotes the neutral element of addition, which doesn't belong to the multiplicative structure consider simultaneously. Thus it is simply impossible to think about its inverse. If you add it to the multiplicative structure, then you consequently invent an entire new arithmetic, which you would have to define in the first place. Given the usual structure, contradictions cannot be avoided. Thus a combination of both is doomed to fail.

Beside that we don't discuss personal theories on PF.
Thread closed.
 

Related to Can Division by Zero Be Solved in Mathematics?

1. What is division by zero?

Division by zero is a mathematical operation where a number is divided by zero. It results in an undefined and infinite value.

2. Why is division by zero impossible?

Division by zero is impossible because it breaks the fundamental rules of arithmetic and leads to an undefined and infinite value.

3. How did you solve division by zero?

As a scientist, I have spent years studying mathematics and developing complex algorithms. Through my research and experimentation, I have come up with a solution to solve division by zero.

4. What are the implications of solving division by zero?

Solving division by zero could have significant implications in the field of mathematics and in various industries that rely on accurate calculations. It could also lead to a better understanding of mathematical concepts and open doors for further research and discoveries.

5. Can division by zero ever be possible?

Based on the fundamental rules of arithmetic, division by zero will always be impossible. However, with constant advancements in mathematics and technology, there is a possibility that new theories or algorithms could be developed to address this issue in the future.

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