Divide By Zero: Is It Ever Logical Not To?

[gregmead]

then the line would have no slope because change in y would also be zero

Edit: read next post

 

[eNathan]

then the line would have no slope because change in y would also be zero

That is exatly my point. $$\frac {y_1} {x_1}$$ Or $$\frac {y_2} {x_2}$$ have to result in 0, and then after you add the interception point of y you can get your straight line.

 

[gregmead]

Edit: sorry misunderstood

if dx=0 then the slope WILL be infinite, eg undefined, not equal to 0. It will be vertical, which when you think about what slope means and what the graph is telling you, makes sence.

 

[Moo Of Doom]

Since when is slope $$\frac{y_1}{x_1}-\frac{y_2}{x_2}$$? Isn't it $$\frac{y_1-y_2}{x_1-x_2}$$?

In that case, if the two x values are the same, then the slope is vertical. Vertical slope is orthogonal to zero slope, so you can hardly say that division by zero results in zero.

 

[C4rlne55]

Since when is slope $$\frac{y_1}{x_1}-\frac{y_2}{x_2}$$? Isn't it $$\frac{y_1-y_2}{x_1-x_2}$$?

In that case, if the two x values are the same, then the slope is vertical. Vertical slope is orthogonal to zero slope, so you can hardly say that division by zero results in zero.

you have a point there, but if the two x values are the same then what exactly are we trying to prove? that the graph will tend to infinity in the y direction as the function approaches the limit where the gradient is $$\frac{1}{0}$$, ie undefined, ie a number much greater than we can work with, ie the gradient is mahoosive, ie vertical?

which has been shown on oh so many graphs over the years, for example the classical y=$$\frac{1}{x}$$, where at the point x=0, the function is undefined and has an asymptote

it is worth pointing out gregmead's point on the fact that $$\frac{1}{0}$$ is undefined as opposed to "infinity". "infinity" is actually a bungled job on the part of physicists, because they like to say (for example) bring a charge in from infinity... well, that raises the question "what does that mean?"

 

[hey.like]

The error is in the zero

The sorry is a absolute zero being true.
In math, it is right.
In nature, it is ease to division but in math or phys is not right.
The sorry as God in another world.