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First of all, thanks for this brain teaser
I think our brains have to struggle a lot to answer the questions
a.) What is the largest negative integer number
b.) What is the smallest negative integer number
What surprises me is when I am asked the questions (which I asked myself after reading your puzzle):
a.) Is -1 greater than -2?
vs
b.) Is -2 less than -1?
Myself can answer question b.) much more easily 
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OriginalGriff wrote: It seem that many of us are convinced that -∞ is larger than 0
That has me worried about the state of our profession! 
Disclaimer: I didn't read all of the >50 replies to your original message, considering the solution you posted in the ≈5th message as self-evident and not a reason for debate. After that point I just shook my head in disbelief. 
Mircea
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In my case (non native english speaker) "large" is for me more associated with size, not value.
That's why I would usually think first on the biggest module in negative, meaning -∞.
But... as I have had a lot of such tricky questions, I tend to wait a second, put back the obvious answer and pay a lot of more attention to the wording while activating the paranoic mode. So at the end I found the right solution.
M.D.V. 
If something has a solution... Why do we have to worry about?. If it has no solution... For what reason do we have to worry about?
Help me to understand what I'm saying, and I'll explain it better to you
Rating helpful answers is nice, but saying thanks can be even nicer.
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I (native speaker) would agree there. To me, there's a difference between "greater" and "larger", and between "less" and "smaller". Greater/less include the sign whereas larger/smaller refer to the absolute magnitude.
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And, as I stated in JavaScript:
-1 > Number.NEGATIVE_INFINITY;
If you only believe C# then:
Console.WriteLine(-1 > Double.NegativeInfinity );
Since programming languages do model mathematics I think this should help to understand this.
However, I am no mathematician and defer to anyone with a Math degree on this. 
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OriginalGriff wrote: * Zero is neither positive nor negative because the definition of both those terms stems from the direction of X from 0.
Well that's bullpucky. I've been looking around and I have seen only circular definitions/properties for "positive" -- first they assume that zero is not positive and then they define a property which may or may not be consistent with that definition.
Zero is positive. And so am I.
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If 0 should be positive (or negative), then the whole chemistry/quantum theory has a problem?
[Edit]
Limit value considerations are a different topic, whether one approaches a limit value from negative or positive
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PIEBALDconsult wrote: Well that's bullpucky. I've been looking around and I have seen only circular definitions/properties for "positive"
Not sure I understand your point.
There are many assumptions and term definitions in mathematics. Proofs are then based on both of those. If the terms/definitions are not accepted/understood then the proof becomes invalid (at least for one person.)
I am rather certain that negative and positive are and always have been definitions. No one attempts to prove them.
Not to mention of course that semantics of language makes this even more confusing. For example provide a definition for the word 'table' which includes all tables but excludes all other objects.
Because of that people are always going to be limited in attempting to provide exact definitions. Including in mathematics.
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Yes. The Mariana Trench is deeper than Mount Everest is high. But that doesn't mean the trench is "bigger".
"Before entering on an understanding, I have meditated for a long time, and have foreseen what might happen. It is not genius which reveals to me suddenly, secretly, what I have to say or to do in a circumstance unexpected by other people; it is reflection, it is meditation." - Napoleon I
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Mount Everest isn't high at all; it's at ground level.
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Perfect, it might have the highest/tallest peak, still at ground level... 
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it makes sense.
the problem is the term "largest negative integer".
Does the "largest non-negative integer" = infinity ? if so, then the reverse would be "largest negative integer" which by symmetry would be -infinity. The problem is mixing language and mathematics.
3rd grade math revisited.
"A little time, a little trouble, your better day"
Badfinger
modified 15-Feb-24 15:04pm.
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Quote: 1 was the last, so it's the smallest positive number.
Everyone here has agreed on that!
Not the flat earthers.
(they abound) 
>64
It’s weird being the same age as old people.
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And again I balk. "greater than" and "largest" are not synonymous for me, and "largest", when speaking of negative numbers, is non-sensical because negative things don't have "largeness." 
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So ... you can't have a "large student debt"? 
"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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Large or smaller is a perception as it might be greater than the next or it might be less tahn the next, philosophy kicking in now sorry...
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I never doubted for a minute that you were correct, I just didn't think hard enough about it.
The difficult we do right away...
...the impossible takes slightly longer.
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Very interesting riddle, almost got a brain freeze  If you read carefully, the answer to get to 30 is quite obvious, unfortunately our brains are not wired that way.. 
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My first reaction, too. The first time I encountered this puzzle was an oral presentation. Made for some interesting notes, until one does the math correctly. The key is "where is the money", not "who spent what".
"A little time, a little trouble, your better day"
Badfinger
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Bringing QA experience to the Lounge!
"In testa che avete, Signor di Ceprano?"
-- Rigoletto
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Maybe - if you change "non-positive value" in your last sentence to "non-negative value".
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Oops!
Fixed
"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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I'm not sure about your explanation, but I sense you are making the mistake I referred to yesterday, viz. basing your argument on the way number theory is implemented in the computer languages with which you are familiar, rather than on formal number theory itself. To answer the question we need the advice of pure mathemeticians on how magnitude of negative numbers is defined. How computers deal with it is clouded, as usual, by practicalities and compromise. However I doubt if there are any pure mathematicians lurking in this forum!
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Just as a side winder regarding the math's behind this, why is it that binary only runs on 0 (zero) and 1's with 0 being the neutral number then and not why use -1 0 0 1 1 0 -1 as binary.
Maybe I should just go Google first as this is above my paygrade... ?
And so I found this also relating to largest and smaller compared to bigger and less, sorry - Binary Negative Numbers![^]
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