A gentle puzzle I was just asked.
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Smallest positive integer = 1 Largest negative integer = -1 Difference is 2.
This person is absolutely correct. In the field of mathematics, the largest negative integer is -1. Therefore 1 - (-1) would indeed be 2.
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Smallest positive integer = 1 Largest negative integer = -1 Difference is 2.
My brain went to 2s complement, and also considers largest negative int to be -128 for 8 bits, -32768 for 16 bits. As someone else said, my creditors consider think I owe them a larger amount if it's $32,768 instead of $1. But then my brain fried.... I know it would over or underflow, but exactly how? Hmm.... I've spent so many years programming to avoid such overflows that I no longer remember. Does it depend on the compiler? C# example: Int16 a = 1; Int16 b = -32768; Int16 c = (Int16)(a - b); C winds up being -32767, which means it wound up doing the 16 bit equivalent of (0001 - 1000) = 1001 in binary. The LSB being one makes sense to me. The MSB being one is not so obvious.
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Depends on context. See Is zero positive or negative?
Bond Keep all things as simple as possible, but no simpler. -said someone, somewhere
Zero is definitely not negative. And it's not imaginary either. If it's neither positive nor negative, then it must also be neither imaginary nor real. If we accept zero as a real, then we must conclude that zero is positive.
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It can be positive, negative or unsigned depending on the representation and how it is used. Fnu
As a particular representation, perhaps. But what about as a pure concept?
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I think it's a bad mistake to assume that a computer implementation of a mathematical concept provides a correct definition, especially at the limits. But I agree that mathematically -1 is larger than -2. It's the distance from the extreme left of the number line (-infinity) that illustrates this. And zero is neutral, neither positive nor negative. And we're relying on ChatGPT for truth now? Lord help us!
haughtonomous wrote:
a bad mistake to assume that a computer implementation of a mathematical concept provides a correct definition,
Oh, wow, there's a lot packed into that, because it would be odd if computer languages were also wrong about mathematical concepts, wouldn't it? Logic would be wrong and all kinds of things. Of course, I do understand that a language only models mathematical concepts. But it would be a huge exposure if programming languages didn't define mathematical concepts properly, i think.
haughtonomous wrote:
And zero is neutral, neither positive nor negative.
I agree 100% on that.
haughtonomous wrote:
And we're relying on ChatGPT for truth now?
No, I'm not depending on it. I am curious about what chatGPT thinks tho, because, in my experience, it hallucinates (lies) often.
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I don't - we have dictionaries to do that: :-D
Quote:
largest Definitions from the GNU version of the Collaborative International Dictionary of English. (adjective) Greatest in size of those under consideration. (adjective) maximal. from Wiktionary, Creative Commons Attribution/Share-Alike License. (adjective) Superlative form of large: most large.
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony "Common sense is so rare these days, it should be classified as a super power" - Random T-shirt AntiTwitter: @DalekDave is now a follower!
That is no help whatsoever for your mathematical usage here.
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What is the smallest positive integer minus the largest negative integer?
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony "Common sense is so rare these days, it should be classified as a super power" - Random T-shirt AntiTwitter: @DalekDave is now a follower!
The algebraic symbol > is usually pronounced (in English) "greater than", rather than "larger than", and I think some of the ambiguity of the question and its interpretation lies in the specific words used. If the question had specified "greatest negative number" rather than "largest negative number", it might have elicited different answers. -1 > -∞, but is -1 "larger" than -∞ ? How many bits does it take to encode each "value"? Rich Leyshon's proposition of speeding a car in reverse to avoid a ticket, and the likely outcome, seems apt.
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Start with two bit signed numbers and work your way up from there ... :-D That always made me laugh - back in the day when CD players were the Bee's Knees they proudly announced the kit contained a "1 bit DA converter" on the adverts (and the player, normally).
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony "Common sense is so rare these days, it should be classified as a super power" - Random T-shirt AntiTwitter: @DalekDave is now a follower!
OriginalGriff wrote:
they proudly announced the kit contained a "1 bit DA converter"
Which was entirely correct. Sigma/Delta DA (and AD) converters are indeed 1-bit converters that use crazy oversampling plus noise-shaping to produce an analog output that has the same resolution as a 16 or 24 bit "classical" converter :) . The introduction of sigma/delta converters removed a whole class of non-linearity issues with classical converters.
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What is the smallest positive integer minus the largest negative integer?
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony "Common sense is so rare these days, it should be classified as a super power" - Random T-shirt AntiTwitter: @DalekDave is now a follower!
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As a particular representation, perhaps. But what about as a pure concept?
I can see one possible definition mathematically. In Number Theory a Number Line starts with the sequence 0,1,2... That allows one to define addition. At this point there is no 'positive' because there is nothing but that. So no categorization is possible. To define subtraction one must then add to the above Number Line with the following sequence -1, -2, ... So in terms of categorization I can certainly see positive including zero where negative does not. That said however in googling certainly there are many answers addressing Number Theory that state that zero is neither positive nor negative.
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I think it's a bad mistake to assume that a computer implementation of a mathematical concept provides a correct definition, especially at the limits. But I agree that mathematically -1 is larger than -2. It's the distance from the extreme left of the number line (-infinity) that illustrates this. And zero is neutral, neither positive nor negative. And we're relying on ChatGPT for truth now? Lord help us!
haughtonomous wrote:
bad mistake to assume that a computer implementation of a mathematical concept provides a correct definition,
A definition is just that. One can accept it or reject it. That is exactly how mathematics and even logic works. Other than that it certainly not possible to prove a definition in any way. Myself I would accept an authoritative source but what is that source exactly? (I have been looking for such a source related to this thread.)
haughtonomous wrote:
And we're relying on ChatGPT for truth now?
People assume a vast array of definitions, assumptions and proofs every day. They certainly do not prove them. Someone that attempted that would probably need to be locked up. (Lets prove F=ma every day by standing in front of a moving car.) So what source should one use? What source are you relying on for Number Theory (which is what this falls into.) As an example myself I would really like to also find an authoritative source that shows that the world is a sphere. Certainly seem people claim it, then cite various ways to prove it (without themselves actually proving it.) I have also read articles that demonstrate that certain attempts to prove it are flat are just wrong. Which of course does not prove it is a sphere either. So I am left with just assuming that it is a sphere.
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haughtonomous wrote:
bad mistake to assume that a computer implementation of a mathematical concept provides a correct definition,
A definition is just that. One can accept it or reject it. That is exactly how mathematics and even logic works. Other than that it certainly not possible to prove a definition in any way. Myself I would accept an authoritative source but what is that source exactly? (I have been looking for such a source related to this thread.)
haughtonomous wrote:
And we're relying on ChatGPT for truth now?
People assume a vast array of definitions, assumptions and proofs every day. They certainly do not prove them. Someone that attempted that would probably need to be locked up. (Lets prove F=ma every day by standing in front of a moving car.) So what source should one use? What source are you relying on for Number Theory (which is what this falls into.) As an example myself I would really like to also find an authoritative source that shows that the world is a sphere. Certainly seem people claim it, then cite various ways to prove it (without themselves actually proving it.) I have also read articles that demonstrate that certain attempts to prove it are flat are just wrong. Which of course does not prove it is a sphere either. So I am left with just assuming that it is a sphere.
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haughtonomous wrote:
bad mistake to assume that a computer implementation of a mathematical concept provides a correct definition,
A definition is just that. One can accept it or reject it. That is exactly how mathematics and even logic works. Other than that it certainly not possible to prove a definition in any way. Myself I would accept an authoritative source but what is that source exactly? (I have been looking for such a source related to this thread.)
haughtonomous wrote:
And we're relying on ChatGPT for truth now?
People assume a vast array of definitions, assumptions and proofs every day. They certainly do not prove them. Someone that attempted that would probably need to be locked up. (Lets prove F=ma every day by standing in front of a moving car.) So what source should one use? What source are you relying on for Number Theory (which is what this falls into.) As an example myself I would really like to also find an authoritative source that shows that the world is a sphere. Certainly seem people claim it, then cite various ways to prove it (without themselves actually proving it.) I have also read articles that demonstrate that certain attempts to prove it are flat are just wrong. Which of course does not prove it is a sphere either. So I am left with just assuming that it is a sphere.
I still remember one geometry lesson about the Greeks measuring shadows at high noon in two cities at different latitudes on the same day and using that to calculate the radius of the earth. Similar to the trick of using your own shadow to measure the height of a tree base on the tree’s shadow.
