
"A little time, a little trouble, your better day"
Badfinger





Gee  that is exactly like me!
I learned a lot from it. One thing was skimming: When shelving books, I saw far too many that I'd like to read, so twice a week (I worked two nights a week a the library), I brought 1012 books with me home. Of course I didn't have time to read them all thoroughly, but I didn't want to just bring them back. So I learned to at least go rapidly through all those I couldn't read every word of, to pick up the main points, see which answers it could provide the day I needed it. I'd say that was very valuable learning!
Actually, I considered switching from software development to becoming a librarian at the technical university; I was offered a paid learning position that would lead to a degree. It would reduce my yearly income by about 10,000 Euros, which was quite significant in the late 1980s, and I had just become a daddy, so I turned the offer down. Some times I regret that I did.
I don't think that library was computerized until it was caught in a fire, burning to ashes all the books on the shelves, including the two or three incunables the head librarian once showed me in the back room. She did not allow me to hold them; she wore white cotton gloves herself when handling them. But they were lost in the fire.
The only good thing is that while the old library was really old and backwards, the new one that was build was really appealing, with practical solutions and lots of modern facilities that would have been difficult or impossible to install in the old building.
Religious freedom is the freedom to say that two plus two make five.





trønderen wrote: The only good thing is that while the old library was really old and backwards, the new one that was build was really appealing In 1977, the middle of my tenure, a new building was constructed and all of our inventory was moved. That building is now being renovated and expanded, a little over 40 years later.
The original building was a Carnegie library[^] constructed by philanthopist Andrew Carnegie. It still stands and is in relatively good condition. It has been used for several businesses and even a private residence at one point. At the moment it is empty, waiting for someone with resources and inventive ideas to bring it back to life.
Software Zen: delete this;





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 nonpositive 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 nonnegative 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 Tshirt
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modified 16Feb24 4:00am.





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".





How about π: it has lots of figures and a minus sign
Mircea





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.





e^iπ is the largest negative integer, I'd say.
modified 16Feb24 5:08am.





e^{iπ}
FTFY.
Software Zen: delete this;





Eye thang ewe.





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;





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).






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 Tshirt
AntiTwitter: @DalekDave is now a follower!






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.





So what you’re saying is, mathematical proofs are like statistics, you can make them suit your narrative





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.)






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





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 selfevident and not a reason for debate. After that point I just shook my head in disbelief.
Mircea





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.





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.





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.





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.



