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It seem that many of us are convinced that -∞ is larger than 0 so I thought I'd try and explain why that isn't the case, even though it does seem to make sense.
Let's look at what "greater than" actually means (in all cases I'll use integers but it's exactly the same for floating point numbers).
1 is greater than 0, 2 is greater than both 1 and 0, 3 is greater than 2, 1, and 0, and so on: the general case is "if you add a positive number* to a value, you get a value that is greater than the original":
X + n > X where n is any positive number.
Similarly, "less than" comes down to:
X - n < X where n is any positive number.
And it works:
2 > 1 because 1 + 1 == 2; 3 > 1 because 1 + 2 == 3; ...
1 < 2 because 2 - 1 == 1; 1 < 3 because 3 - 2 == 1; ...
And we can use "greater than" and "Less than" for find maxima and minima for a set of numbers.
We can find the smallest positive number by taking any positive number as a starting point and repeatedly subtracting 1 until we reach a non-positive value (which will be zero): 1 was the last, so it's the smallest positive number.
Everyone here has agreed on that!
But when we look for the largest negative number it seems that some people are mistaking the absolute magnitude of a value for the value itself, and saying that the largest negative number is -∞
But that's not the case: just as numbers get smaller as you approach 0 from the positive side, they don't start getting bigger again as you move away into the negative side:
1 > 0; 1 > -1; 1 > -2
Slide that sideways and it's clearer for negative numbers:
0 > -1; 0 > -2; 0 > -3
-1 > -2; -1 > -3; -1 > -4
So to find the largest negative number, we start with any negative number as a starting point and repeatedly adding 1 until we reach a non-negative value (which will be zero): -1 was the last, so that's the largest negative number.
Make sense?
* Zero is neither positive nor negative because the definition of both those terms stems from the direction of X from 0.
"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
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modified 16-Feb-24 4:00am.
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I don't think anyone doubted that -1 is the greatest negative integer. It is just that the concept of "large negative" can be easily interpreted by "a number with a lot of figures and minus sign in front of it".
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How about -π: it has lots of figures and a minus sign 
Mircea
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You are evil... 
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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e^iπ is the largest negative integer, I'd say.
modified 16-Feb-24 5:08am.
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eiπ
FTFY.
Software Zen: delete this;
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Eye thang ewe.
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You're welcome... I think.
Kind of sounds like an indecent proposal to a sheep, but to quote the immortal Marty Feldman, "Suit yourself; I'm easy."
Software Zen: delete this;
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A simple method I use is:
If number A is to the right of another number B on the usual number line, then A is larger of the two. Otherwise B is larger.
Consequently the largest of a set of numbers is the rightmost on the number line.
(Of course, two numbers can both be equal, in which case this question doesn't arise).
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I can't explain that, it involves division and I can't do that. 
"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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Paul6124 wrote: on to infinity equals minus 1/12
As it says "only equals -1/12 because the mathematicians redefined the equal sign."
You can also prove other things by ignoring and/or redefining terms and assumptions in mathematics.
For example it is generally accepted that you cannot prove in Euclidean geometry that parallel lines do not intersect. However you can prove that if you assume that a right triangle has a 90 degree angle. So trade one assumption for another.
So in terms of the prior post one can redefine the problem by asserting that negatives can be bigger if the absolute value is bigger. Thus redefining what 'bigger' means in terms of the standard for Number Theory.
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So what you’re saying is, mathematical proofs are like statistics, you can make them suit your narrative
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Paul6124 wrote: you can make them suit your narrative
lol - yes.
The posted link provides a complex example but people have been proving things for a long time by ignoring what divide by zero means. (Long time in my case means I saw such a proof in grade school which meant it existed quite some time before that even.)
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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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