
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.





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





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.





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





Mount Everest isn't high at all; it's at ground level.





Perfect, it might have the highest/tallest peak, still at ground level...





it makes sense.
the problem is the term "largest negative integer".
Does the "largest nonnegative 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 15Feb24 15:04pm.





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.





And again I balk. "greater than" and "largest" are not synonymous for me, and "largest", when speaking of negative numbers, is nonsensical because negative things don't have "largeness."





So ... you can't have a "large student debt"?
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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...





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.






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..





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".
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Badfinger





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Maybe  if you change "nonpositive value" in your last sentence to "nonnegative value".





Oops!
Fixed
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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!





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![^]





oh no this has prompted me to post for the first time ever...
> the general case is "if you add a positive number to a value, you get a value that is greater than the original"
That is your postulate, not a fact or proof. 1 is greater than 2 only if you assume this is true.
I propose another: To divide a quantity or object in half is to produce two halves that are each smaller than the original whole. Divide a number in half, the result is the smaller number.
> Let's look at what "greater than" actually means...
We all know language is ambiguous. It could actually mean many different things. Of course no one is arguing that (1 > 2) doesn't evaluate to true in your programming language of choice* That's just pragmatic.
*except maybe c++ in some cases...





The formal mathematical proof that 1 + 1 = 2 runs to 360 pages of arcane symbols, and I don't understand a single page of it. I'm not going to try and modify that to formally prove X + n > X where n is a positive value because that proof would derive from 1 + 1 = 2 .
Instead, I suggest you show any example which is consistent with 1 + 1 = 2 where X + n <= X where n is a positive value . If you are right and I am wrong (which I'm fully prepared to believe) it should be simple for you
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That is simple: you have a hole in the ground and add a positive amount of soil to it. Is the hole now bigger or smaller? The hole is negative volume.
Divide that hole in half, the half hole is smaller than the whole hole.





tl;dr
"larger" is ambiguous
"larger" can mean "greater than"
"larger" can mean "greater magnitude than"
And that is the issue. English is fickle.





They fixed my issue!
A most joyous day indeed!



