Reminds me of an old aphorism we had in college:

2 + 2 = 5, for very large values of two and very small values of five.​

This code proves that 2 + 2 actually equals 5:

num1 = 2.5
num2 = 2.5
num3 = num1 + num2
print "%d + %d = %d" % (int(num1), int(num2), int(num3))

Output:

2 + 2 = 5

Of course, there's some trickery involved.

 

Someone should pay these judges using half a check. See how they feel about "one" then

I like the fact that it would be the first half he gets.

"1" is not one = my bank account.

kv

 

The #1 is very important (as well as zero) in all aspects of maths. They're my two favourite numbers (though zero being a number, in my eyes, is questionable).

My definition of #1 is an entity. It can be comprised of anything but its foundation is a single whole (let's say a unit for a basis) that is "masked equality" for further operations. For example: (a/b) x (b/a); (ab) / (ab) are typical operations we use in EE. The magnitude of a unit vector is 1 is another.

In some instances we adopt zero to achieve "masked equality". Namely, for a basic example, ax^2 + bx + c = 0 = (x - q)(x - p)

 

(though zero being a number, in my eyes, is questionable).

I say zero is a number because it is the thing you use when you want to use a number and no other number will work.

One is also my favorite number ... now that I'm divorced.

 

The purpose of 1 is to set the scale.

 

The #1 is very important (as well as zero) in all aspects of maths. They're my two favourite numbers (though zero being a number, in my eyes, is questionable).

My definition of #1 is an entity. It can be comprised of anything but its foundation is a single whole (let's say a unit for a basis) that is "masked equality" for further operations. For example: (a/b) x (b/a); (ab) / (ab) are typical operations we use in EE. The magnitude of a unit vector is 1 is another.

In some instances we adopt zero to achieve "masked equality". Namely, for a basic example, ax^2 + bx + c = 0 = (x - q)(x - p)

Okay, so now apply that to something that is related to the court case. Your neighbor borrows 1 cup of sugar. You pay your neighbor back 1 cup of sugar. You neighbor claims that you still own them some sugar. What constitutes "1 cup of sugar"?

 

This cup is a variable I could physically touch. What constitutes "1 cup of sugar" and the "volume of sugar" received are two different things.
As a party trick, I could show you 1=0, but it can be easily proved wrong.

 

This cup is a variable I could physically touch. What constitutes "1 cup of sugar" and the "volume of sugar" received are two different things.
As a party trick, I could show you 1=0, but it can be easily proved wrong.

There are many ways to "prove" that 1=0 (or something similar). Almost all of them involve some place where you are dividing by zero. The one I like the best doesn't -- of course it has a fundamental error in it, but it is one that most people really struggle to spot.

 

There are many ways to "prove" that 1=0 (or something similar). Almost all of them involve some place where you are dividing by zero. The one I like the best doesn't -- of course it has a fundamental error in it, but it is one that most people really struggle to spot.

Well... let's hear it!

 

Well... let's hear it!

Okay.

If we add N to itself N times, we have N^2.

\(
N \; + \; N \; + \; N \; + \; ... \; + \; N \text{ (N terms)}
\;
= \; N \(1 \; + \; 1 \; + \; 1 \; + \; ... \; + \; 1 \) \text{ (N terms)}
\;
= \; N \( N \)
\;
= \; N^2
\)

Take the derivative of both sides with respect to N

\(
N^2 \; = \; \( N \; + \; N \; + \; N \; + \; ... \; + \; N \) \text{ (N terms)}
\)

\(
\frac{dN^2}{dN} \; = \; \frac{d}{dN} \( N \; + \; N \; + \; N \; + \; ... \; + \; N \) \text{ (N terms)}
\)

\(
\2N \; = \; \( \frac{dN}{dN} \; + \; \frac{dN}{dN} \; + \; \frac{dN}{dN} \; + \; ... \; + \; \frac{dN}{dN} \) \text{ (N terms)}
\)

\(
2N \; = \; \(1 \; + \; 1 \; + \; 1 \; + \; ... \; + \; 1 \) \text{ (N terms)}
\)

\(
2N \; = \; N
\)

\(
\therefore \; \; 2 \; = \; 1
\)

 

I wonder what the judges would decide if I took a case before them where I had ordered one cake but received a half eaten cake. As MikeML says above, they need to distinguish integers from reals.

Reminds me of a mathematician, a physicist and an engineer asked what 2 + 2 equals

The mathematician says 4

The physicist says somewhere between 3.9 and 4.1

The engineer says 4 but lets call it 8 to be on the safe side

The accountant says: "What number did you have in mind?"

 

Hi,

I see this not as much as a philosophical issue as a practical issue.

I think everyone here has experienced this very same thing in their chosen hobby.
For example, we've all probably used a resistor of 1 Ohm at one time or another.
Did we measure it to make sure it was 1.000000 Ohms? I doubt it. There is always a tolerance but we often ignore it when the context is clear. We know we didnt mean 0.0 ohms or 2.0 ohms, but there is often a good chance that 0.9 ohms or 1.1 ohms would also work.

The problem comes in though when you design a circuit and get a patent for it that uses a 1 Ohm resistor. What if another company comes along and creates the same circuit with a resistor that is 0.99 ohms instead. Are they subject to the first patent? If not, then what about 0.999 ohms or 1.001 ohms? How about 0.8 ohms or 1.2 ohms?
Someone somewhere has to decide what is going to be acceptable as a *different* value. There has to be some significance to this or else the second party could use 0.99 ohms and say they have their own unique design. It should not be too significant, yet significant enough such that it will be more clear that it is not the same thing. Remember the 'rounded corner' phone issue not too long ago. What constitutes a rounded corner.

 

But this wasn't the case of a product that is patented to do X happening to use a particular concentration of an ingredient. It was a case of the patent specifically stating in its claims that the patent covered solutions between X percent and Y percent. It's very possible, even likely, that the range claimed in the patent already included a buffer zone beyond the range of concentrations they were really trying to protect.

 

The article is completely clear. Lawyers, linguists and Politicians have been setting rules for commerce since the Magna Carta, the Reinheitsgebot and The Uniform Commercial code.

Quality testing in the Chemical industry uses the common rounding assumptions that the judges used unless the standard specification uses decimal places to describe the assay or contaminant concentration.

It is fun to criticize lawyers and judges making decisions about "science" but patents are not science, they are business. That is why the National Institute of Standards and Technology (NIST) - formerly, NBS, and the Patent and Trademark Office are part of the Commerce Department in the US.

I see nothing wrong with their decision. Otherwise, I would have competitors claiming they are not using 1-3% poo-poo-manindium in their formulation, they only have 0.999999999%. How do I protect myself from that and how do I argue that some of my competitor's batches exceed 1% based on lot-to-lot variation. Nice to see someone put and end to hair-splitting assholes who would rather copy than innovate.

 

.

Lawyers, linguists and Politicians have been setting rules for commerce since the Magna Carta, the Reinheitsgebot and The Uniform Commercial code.

Here's a bit of history that I thought had been true for a while... until I bothered to check it out for myself. Turns out, sometimes there's a bit of truth to urban legends:
http://www.snopes.com/media/notnews/pi.asp

 

Or maybe I just overthink things...

No, but you do ask difficult questions.

 

This is a question worth considering and also a meaningful problem.

 

.Here's a bit of history that I thought had been true for a while... until I bothered to check it out for myself. Turns out, sometimes there's a bit of truth to urban legends:
http://www.snopes.com/media/notnews/pi.asp

And you thought this bit of silliness had been try [edit: "true" -- stupid autocorrect] why?