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The sign greater than "$>$" represents the quantity of one number more than another number. However the same sign is used to know the direction of a number on the numberline ( with respect to an another given number ). So $5 > -5$ holds true.

However, in reality there is no difference in the quantity of two numbers. They are just on opposite side of origin. Isn't it an ambiguous trend to calculate in math ? Is there any other way to represent the same thing that makes sense?

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  • $\begingroup$ Have a look at the formal definition of $>$ and perhaps also absolute values. $\endgroup$ – John Smith Aug 5 '14 at 8:25
  • $\begingroup$ If you owe me $\$5$ that's a big difference from me owing you $\$5$. Let's say the $\$5$ bill is sitting between you and me. Someone has just taken it out of his wallet. Someone is about to put it into his wallet. After that transaction, one of us will have $\$5$ more and one of us will have $\$5$ fewer. $\endgroup$ – James47 Aug 5 '14 at 22:14
  • $\begingroup$ Any thoughts on the comments and answers you have received, Vishwas? $\endgroup$ – Gerry Myerson Aug 6 '14 at 13:18
  • $\begingroup$ Well, i think, my question was misunderstood. My question was particularly on the confusion posed by ">" greater-than symbol. All the answers assume that there is no confusion. And saying one thing is different from another is same as saying one thing is greater than another. $\endgroup$ – Vishwas G Aug 7 '14 at 14:17
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The "quantity" of $5$ and $-5$ is not the same. $5$ is greater than $-5$. For example, a temperature of $5$ degrees is warmer than a temperature of $-5$ degrees.

What you are taking about is the absolute values of numbers, which are equal to the distances from the number to $0$. So the absolute value of $-5$ is equal to $|-5|=5=|5|$. The absolute values of $-5$ and $5$ are the same (the numbers themselves have the same "size"), although still, $5$ is larger than $-5$ (the quantities these two numbers describe are different, $5$ describes a larger quantity).

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$a>b$ means $a-b$ is positive, nothing more, nothing less --- and nothing ambiguous about it. $-2>-17$ because $-2-(-17)=15$ is positive, even though 17 is farther from the origin than 2. You'll have to be more clear about what exactly it is that you think doesn't make sense.

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  • $\begingroup$ I was of the opinion, whenever you put ">" between a and b, like a > b. It only means a "is greater than" b, in quantity. Why it's named as "greater than" operator otherwise ? $\endgroup$ – Vishwas G Aug 7 '14 at 14:22
  • $\begingroup$ If your opinion leads you to write $-17>2$, then I suggest it's time for you to re-evaulate your opinions. That's just not the way that symbol is used. $2$ is greater than $-17$, in the sense that if you have 2 rupees your wealth is greater than that of someone who is 17 rupees in debt. $\endgroup$ – Gerry Myerson Aug 8 '14 at 0:07

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