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eNathan
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Can somebody please tell me any case where it is logical to NOT divide by zero? I know division by zero is illogical itself, but usually when you divide by zero the result should be zero anyway.
cronxeh said:Try dividing 1 by 0.000000000000000000000000000001. Big number?
Now try 1/(10^-99999) - is that bigger than 0 or close to infinity?
eNathan said:Can somebody please tell me any case where it is logical to NOT divide by zero? I know division by zero is illogical itself, but usually when you divide by zero the result should be zero anyway.
HallsofIvy said:Where did you get the idea that "usually when you divide by zero the result should be zero anyway." I can't imagine any situation (except under some condition where you have 0/0 but you don't seem to be talking about that) where dividing by 0 could reasonably be interpreted at resulting in 0.
Some people say, loosely, that dividing by 0 results in infinity- but surely not 0!
eNathan said:Oh ye, if [tex]\frac {x} {0} = \infity[/tex] then [tex]x != \frac {x} {\frac{1}{0}} [/tex]
gregmead said:your statement x/0 = Infinity is not technically correct, sorry I'm not good at latex so you'll have to make do with shoddey normal writing.
Its better to say that x/0 is underfined or things start getting a bit messed up
Moo Of Doom said:You don't really want to do arithmetic operations with [tex]\infty[/tex], but yeah generally it is true that [tex]a*\infty = b*\infty[/tex] so long as a and b aren't zero.
Icebreaker said:On a similar note, do you consider [tex]lim f(x) = \infty[/tex] (when it is the case) a misleading notation?
gregmead said:I don't see anything wrong with that notation, is this a trick question ? ;-)
Hurkyl said:Even in the extended reals, 1/0 is undefined. The limit as you approach 0 from the positive side is different than if you approach from the negative side, so division cannot be extended continuously to (1,0).
gregmead said:then the line would have no slope because change in y would also be zero
Moo Of Doom said:Since when is slope [tex]\frac{y_1}{x_1}-\frac{y_2}{x_2}[/tex]? Isn't it [tex]\frac{y_1-y_2}{x_1-x_2}[/tex]?
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.
No, dividing by zero is not allowed in mathematics. It is considered undefined and leads to an infinite result.
No, dividing by zero is never logical. It violates the fundamental principles of mathematics and leads to contradictions.
No, there are no real-life situations where dividing by zero is applicable. It does not have any practical meaning or application in the real world.
When dividing by zero in a computer program, an error will occur. This is because computers are programmed to follow the rules of mathematics and cannot perform the operation of dividing by zero.
No, there is no way to approach dividing by zero without getting an undefined result. It is a fundamental concept in mathematics that cannot be altered or manipulated.