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This was the first question that crossed my mind. According to the interweb, it's the size of the absolute value.
Maybe it really depends on what the numbers are representing. On a graph, (-2,-2) is a greater distance from the origin than (-1,-1).
I would rather reverse my car into a lamp post at -1mph than -20!
Of course, doing it the other way round could be a good way out of a speeding fine. If I state I was clocking my speed in a backwards direction then my forward speed would be negative and the further I went above the speed limit, the smaller my speed would be. "Take him down ..."
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Arithmetic Overflow. 
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Smallest positive integer = 1
Largest negative integer = -1
Difference is 2.
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That was my first shot as well, but the answers above cast a big doubt. I am too naive.
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Dat's de bunny! 
Surprising how many people think -2 is bigger than -1. 
"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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Also what I got, mostly as I've had to solve this puzzle in multiple math classes, and was usually the only person to get it right (sadly).
What do you get when you cross a joke with a rhetorical question?
The metaphorical solid rear-end expulsions have impacted the metaphorical motorized bladed rotating air movement mechanism.
Do questions with multiple question marks annoy you???
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I agree with you.
Here's 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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Largest negative. I had not noticed that. Reading correctly is half the battle. 
Well done 
Bastard Programmer from Hell
"If you just follow the bacon Eddy, wherever it leads you, then you won't have to think about politics." -- Some Bell.
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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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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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