What is the difference between $\gg$ and $\gt$ ?
Thank you $\infty$ times.
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The difference is whether or not the left-hand-side is $\infty$ times greater than the right-hand-side. $:$ ^_^ $;;;$ – Jan 03 '14 at 11:21
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of $>>$ means significantly larger than – Quickbeam2k1 Jan 03 '14 at 11:21
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1a >> b means that a is much much larger than b; a > b would just mean that a is larger than b [1.00001 > 1 but 100001 >> 1] – Claude Leibovici Jan 03 '14 at 11:25
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$a \gt b$ means $a$ is greater than $b$ so for example $1.0001 \gt 1$. While $a \gg b$ means $a$ is much larger than $b$. We would not say $1.0001 \gg 1$ but may say $100000 \gg 1$. – Warren Hill Jan 03 '14 at 11:29
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@ClaudeLeibovici This is hardly mathematics. – Did Jan 03 '14 at 11:32
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@WarrenHill Sorry but I would never say $100000\gg1$. – Did Jan 03 '14 at 11:32
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@Did: as measures on a singleton, $100000 \gg 1$ – SBF Jan 03 '14 at 11:33
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@Did. I agree with you but for illustration puroposes with numbers of "human" sizes ... ? – Claude Leibovici Jan 03 '14 at 11:39
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@ClaudeLeibovici Only confuses things. – Did Jan 03 '14 at 11:49
1 Answers
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Imprecisely, we usually say that $a\gg b$ means that $a$ is much larger than $b$. Of course, this seems like it depends a great deal on how you define "much".
I usually only see this notation used in asymptotics: that is, we take $a\gg b$ to mean the same thing as $b=o(a)$, which means that $a=a(n)$ and $b=b(n)$ depend on some $n$, and $$ \lim_{n\rightarrow\infty}\frac{b(n)}{a(n)}=0. $$
Nick Peterson
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