Can we discuss this?

[Boxing Pythagoras]

How many mathematicians does it take to screw in a light bulb?

0.999...

If you're having Math problems, I feel bad for you son.
I got 99 problems, but 0.999... = 1.

[Leonhard]

If you're having Math problems, I feel bad for you son.
I got 99 problems, but 0.999... = 1.

Of course 0.999... = 1, it was a joke.

[Boxing Pythagoras]

Of course 0.999... = 1, it was a joke.

I know-- mine was, too. Mathematical parody of Jay-Z's "99 Problems"

[Juvenal]

I know-- mine was, too. Mathematical parody of Jay-Z's "99 Problems"

The wit of a joke decays exponentially, base 2, with the number of times it's explained.

[Carrikature]

If you're having Math problems, I feel bad for you son.
I got 99 problems, but 0.999... = 1.

I prefer the fencepost version created by Randall Munroe.

[klaus54]

1/0 = [ATTACH=CONFIG]3698[/ATTACH]

1/0 is undefined. Aleph_null ain't. Your answer could just as well be Aleph_n, n in Z+.

Cardinal number vis-a-vis limit.

K54

[37818]

1/0 is undefined. Aleph_null ain't. Your answer could just as well be Aleph_n, n in Z+.

Cardinal number vis-a-vis limit.

K54

1/0 is undefined as a standard.

If we write 1/x and x approaches zero. Then as x approaches zero the value of 1/x approaches infinity.

1 - .999... is either zero or an infinitesimal greater than zero. Depending on the equality. An infinitesimal taken by itself is equal to zero for all practical purposes. And division by zero is undefined for most all practical purposes. And 1 divided by an infinitesimal is equal to infinity. And of course if the infinitesimal is defined as a discrete value, then the division results in a very large number which is not infinite.

[37818]

You can't divide by zero, so it is not equal to aleph zero.

It has been defined that division by zero cannot be done.

I define division by zero as infinite. I really do not care that it is not the standard. I also use a rule for an indeterminate in which the indeterminate becomes the value in an equation which makes the equation equal. And a none equal result is breaking this rule, and is therefore never the valid answer.

Two equations which, for example, create the very same graph. Except on the form of one of the equations has an indeterminate form in it. That indeterminate is defined by the tangent value at that point. And that value for that indeterminate makes the equation equal at that point. This is not your standard algebra.

[Leonhard]

It has been defined that division by zero cannot be done.

I define division by zero as infinite.

Actually you can't coherently define division by zero, for the simple reason of what the definition of what 0 and division is.

Division is defined like this:

For a given number 'a' not equal to '0', there exists a number 'b', such that the equation 'a*b = 1' is fulfilled. We give this number the symbol '1/a', multiplying this number by a scalar c is written 'c/a' and we term this 'c divided by a'.

The number '0' is defined to be a number such that for any 'a' we have that '0*a = 0'.

So if you want to do '1/0' you'd need to find an 'a' such that '0*a = 1', however because 0 has been defined explicitly to be such that this multiplication will always be 0, no matter what 'a' is, you'll get a contradiction. I don't care of its aleph_0 or a aleph_1000000. It will still be a contradiction.

In fact if you accept an exception, any exception, you'd be forced to agree that 0 = 1.

So division by zero remains undefined, otherwise we'd have a contradiction.

Two equations which, for example, create the very same graph. Except on the form of one of the equations has an indeterminate form in it. That indeterminate is defined by the tangent value at that point. And that value for that indeterminate makes the equation equal at that point. This is not your standard algebra.

No, I'm not sure what kind of language you're using, or what exactly you're describing either. You're basically just taking the limit of 1/x as x goes towards zero from the positive direction. This gives +infinity, and if it had been from the negative direction you'd get -infinity. But those symbols simple represent limits, they're not numbers in and of themselves and can't be treated as such.

[Leonhard]

1 - .999... is either zero or an infinitesimal greater than zero.

If you're dealing with the real numbers, then '1 = 0.999...', without any ambiguity, not merely for practical purposes.

[Teallaura]

If you're dealing with the real numbers, then '1 = 0.999...', without any ambiguity, not merely for practical purposes.

Um, aren't real numbers practical?

Yeah, I 'get' the concept but my brain really hates that equation since they are different. It reads as wrong to me - even though I understand why it isn't.

[37818]

Actually you can't coherently define division by zero, for the simple reason of what the definition of what 0 and division is.

Division is defined like this:

For a given number 'a' not equal to '0', there exists a number 'b', such that the equation 'a*b = 1' is fulfilled. We give this number the symbol '1/a', multiplying this number by a scalar c is written 'c/a' and we term this 'c divided by a'.

The number '0' is defined to be a number such that for any 'a' we have that '0*a = 0'.

So if you want to do '1/0' you'd need to find an 'a' such that '0*a = 1', however because 0 has been defined explicitly to be such that this multiplication will always be 0, no matter what 'a' is, you'll get a contradiction. I don't care of its aleph_0 or a aleph_1000000. It will still be a contradiction.

In fact if you accept an exception, any exception, you'd be forced to agree that 0 = 1.

So division by zero remains undefined, otherwise we'd have a contradiction.



No, I'm not sure what kind of language you're using, or what exactly you're describing either. You're basically just taking the limit of 1/x as x goes towards zero from the positive direction. This gives +infinity, and if it had been from the negative direction you'd get -infinity. But those symbols simple represent limits, they're not numbers in and of themselves and can't be treated as such.

The contradiction is do to using indeterminate values to make unequal answers. The unequal answers are never true. Only answers which can be shown to be equal.

0 x 1 = 0. 0 x 2 = 0. 0 x 100 = 0. So 0/0 is indeterminate. In an equation should 0/0 occur, its value is defined by the equality. Otherwise 0/0 by itself is indeterminate.

Infinity ∞
∞/∞ = 0/0 = ∞ x 0 = ∞ - ∞ = indeterminate. The rule is equality. If the result is not equal, then it is not correct usage of an indeterminate.

It has been a while. I have to find an example of what I mean.

[Juvenal]

Um, aren't real numbers practical?

Not for measuring phase shift in a three-phase ac circuit, not that that's relevant to the point here. "Practical" here means "approximate."

Yeah, I 'get' the concept but my brain really hates that equation since they are different. It reads as wrong to me - even though I understand why it isn't.

Some day I'm going to sit you down and explain to you what "=" really means.

[Juvenal]

The most vicious math thread I ever saw was on the old II board.

Topic: Is .9999.... = 1?

Call me jaundiced, but I just can't see this one measuring up.

[Teallaura]

Not for measuring phase shift in a three-phase ac circuit, not that that's relevant to the point here. "Practical" here means "approximate."

You are taking this waaay too seriously...

Some day I'm going to sit you down and explain to you what "=" really means.

So it doesn't mean 'the thing on this side of the = is the same as the thing on the other side'? Mrs Brannen lied?!?!?!!


It still looks way wrong. 1 = 2 looks wrong for the same reason. But I do get why one makes some sense...