A gentle puzzle I was just asked.

Jorgen Andersson

Silly me was thinking in Int32.

Wrong is evil and must be defeated. - Jeff Ello

haughtonomous

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!

BernardIE5317

This should clear things up. Integer - Wikipedia[^]

jarvisa

The smallest positive integer is either 0 or 1 depending on whether 0 is considered positive or not. The largest negative integer is -1. So the answer is 1 or 2. This is not the intent of question but that is the correct answer given how the question was worded.

obeobe

Post-modernism.

MikeCO10

Halfway through my first cup of coffee, this sent me into overthink mode, coming up with everything from infinity to zero. It took some reading of comments to see the correct answer is indeed 2. Great question Griff.

Member 10652083

You have to define 'largest'.

OriginalGriff

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!

jochance

∞ + 1 Because: 1 - (-∞)

mdblack98

Since this is a coding site here are the possibilities for a 32-bit int.

#include #include int main()
{
int pos = 1;
int neg = INT_MIN;
printf("pos=%d neg=%d\n", pos,neg);
printf("pos+neg=%d\n", pos+neg);
printf("pos-neg=%d\n", pos-neg);
printf("neg+pos=%d\n", neg+pos); // yes I know it's commutative but here for completeness
printf("neg-pos=%d\n", neg-pos);
return 0;
}

pos=1 neg=-2147483648
pos+neg=-2147483647
pos-neg=-2147483647 // Hmmm...this seems wrong -- subtracting negative SHOULD add it.
neg+pos=-2147483647
neg-pos=2147483647

Matt Bond

Depends on context. See Is zero positive or negative?

Bond Keep all things as simple as possible, but no simpler. -said someone, somewhere

stheller2

J Tackkett

This person is absolutely correct. In the field of mathematics, the largest negative integer is -1. Therefore 1 - (-1) would indeed be 2.

kholsinger

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.

PIEBALDconsult

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.

PIEBALDconsult

As a particular representation, perhaps. But what about as a pure concept?

raddevus

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.

Member 10652083

That is no help whatsoever for your mathematical usage here.

twhall

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.

Jan Holst Jensen2

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.