Following on from yesterday's little puzzler.
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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." :rolleyes:
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A Lightweight Thread Safe In-Memory Keyed Generic Cache Collection Service A Dynamic Where Implementation for Entity FrameworkSo ... you can't have a "large student debt"? :laugh:
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It seem that many of us are convinced that -∞ is larger than
0so 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 > -2Slide that sideways and it's clearer for negative numbers:0 > -1; 0 > -2; 0 > -3-1 > -2; -1 > -3; -1 > -4So 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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It seem that many of us are convinced that -∞ is larger than
0so 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 > -2Slide that sideways and it's clearer for negative numbers:0 > -1; 0 > -2; 0 > -3-1 > -2; -1 > -3; -1 > -4So 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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It seem that many of us are convinced that -∞ is larger than
0so 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 > -2Slide that sideways and it's clearer for negative numbers:0 > -1; 0 > -2; 0 > -3-1 > -2; -1 > -3; -1 > -4So 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
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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Maybe - if you change "non-positive value" in your last sentence to "non-negative value".
Oops! Fixed :thumbsup:
"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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How about -π: it has lots of figures and a minus sign :laugh:
Mircea
e^iπ is the largest negative integer, I'd say.
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e^iπ is the largest negative integer, I'd say.
e_i_π FTFY.
Software Zen:
delete this; -
e_i_π FTFY.
Software Zen:
delete this;Eye thang ewe. ;-)
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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; -
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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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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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.
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I can't explain that, it involves division and I can't do that. :-D
"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!
The becomes Teh...
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Mount Everest isn't high at all; it's at ground level.
Perfect, it might have the highest/tallest peak, still at ground level... :-D
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So ... you can't have a "large student debt"? :laugh:
"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!
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... :-D
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check out this puzzlement Missing dollar riddle - Wikipedia[^]
"A little time, a little trouble, your better day" Badfinger
Very interesting riddle, almost got a brain freeze :-D 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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It seem that many of us are convinced that -∞ is larger than
0so 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 > -2Slide that sideways and it's clearer for negative numbers:0 > -1; 0 > -2; 0 > -3-1 > -2; -1 > -3; -1 > -4So 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
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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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.)
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It seem that many of us are convinced that -∞ is larger than
0so 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 > -2Slide that sideways and it's clearer for negative numbers:0 > -1; 0 > -2; 0 > -3-1 > -2; -1 > -3; -1 > -4So 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
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...
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Very interesting riddle, almost got a brain freeze :-D 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".
"A little time, a little trouble, your better day" Badfinger
