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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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It seems a lot read it wrongly... The art of understanding a question...
"If builders built buildings the way programmers wrote programs, then the first woodpecker that came along would destroy civilization." ― Gerald Weinberg
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From a comp sci and data representation perspective, yes. Not sure about the math perspective.
Jeremy Falcon
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From a math perspective, zero is neither positive nor negative: Negative number - Wikipedia[^]
"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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It can be positive, negative or unsigned depending on the representation and how it is used. Fnu
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As a particular representation, perhaps. But what about as a pure concept?
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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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1 - (-1) = 1+1 = 2
I’ve given up trying to be calm. However, I am open to feeling slightly less agitated.
I’m begging you for the benefit of everyone, don’t be STUPID.
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Yours is the answer I liked best.
Look at what chatGPT 3.5 says:
ChatGPT: There isn't a smallest positive integer or largest negative integer in the mathematical sense, as integers extend infinitely in both positive and negative directions. The set of integers includes all whole numbers, both positive and negative, and extends infinitely in both directions.
If you're asking about the difference between the smallest positive integer (1) and the largest negative integer (which doesn't exist), it's not a well-defined mathematical operation. The concept of the "largest negative integer" doesn't have a meaningful value in standard arithmetic.
If you have a specific range or context in mind, please provide more details so I can assist you better.
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The largest negative integer is the negative integer that is greater than all other negative integers. hence -1.
Hopefully this isn't devolving into a political conversation.
I’ve given up trying to be calm. However, I am open to feeling slightly less agitated.
I’m begging you for the benefit of everyone, don’t be STUPID.
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MarkTJohnson wrote: The largest negative integer is the negative integer that is greater than all other negative integers.
I thought the same thing.
Also, isn't it interesting that on the other side of 0 that no one had a problem distinguishing the smallest positive integer : which is 1. Aren't all numbers greater than others when the are further to the right of other numbers?
Also, do these people not believe that following are true?
-5000 < -1
-1 > -5000
Then why don't they know that the largest negative integer is -1?
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Check this out. It's JavaScript but...
Number.MIN_VALUE < -1
Number.NEGATIVE_INFINITY > -1
-1 > Number.NEGATIVE_INFINITY
So the largest negative integer is -1. 
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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!
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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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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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I think technically the earth is closer to a geoid.
All kinds of models/templates for mapping, etc.
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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.
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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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10.
Or, possibly, 42.
"In testa che avete, Signor di Ceprano?"
-- Rigoletto
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It's always 42; we just didn't invent the math yet to get us there.
Jeremy Falcon
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We did: fractional bases[^] - but it makes my head hurt trying to think of them ... 
"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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at what bit depth? 
Check out my IoT graphics library here:
https://honeythecodewitch.com/gfx
And my IoT UI/User Experience library here:
https://honeythecodewitch.com/uix
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