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July 9th, 2014, 10:49 AM   #11
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Thanks for the information. Btw, I'm curious about why $\displaystyle \mathbb{Q}$ and $\displaystyle \mathbb{H}$ were chosen to represent rational and irrational numbers, respectively while the other notations are only taken from their initial letters.
$\mathbb{Q}$ for quotient, $\mathbb{Z}$ for Zahlen (German for "number"). $\mathbb{H}$ almost univerrsally stands for the quaternions, with H for Hamilton who discovered them (Q was already taken).

I use $\mathbb{Z}^+$ for the positive integers and $\mathbb{N}$ for the nonnegative integers but this is not universal -- some write $\mathbb{N}$ for the positive integers instead. I've never seen a research paper using $\mathbb{W}$ in this manner.

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July 9th, 2014, 10:51 AM   #12
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Back then, someone is this forum said that if you write log2, then the base number is e. Is that true? Because in my country, if the base number isn't written, it is considered as 10 instead.
In research-level mathematics the base will always be e unless otherwise specified. In computer science an unspecified base may be e but is more often 2 -- but in my experience they often write the base explicitly when the log is not inside a big-O (where any base greater than 1 is equivalent).

Sometimes engineers will use an implicit base 10 but I would strongly recommend against this.
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July 9th, 2014, 01:16 PM   #13
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Not even Malaysia, Timor Leste, or Suriname?

OK, thanks for the informations.

In my country, if it's written as log3, the base number is considered as 10, while if the base number is e, it's written as ln3 (ln stands for "logaritma natural", which literally means "element logarithm").
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July 9th, 2014, 04:08 PM   #14
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Not even Malaysia, Timor Leste, or Suriname?
I couldn't say.

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if the base number is e, it's written as ln3 (ln stands for "logaritma natural", which literally means "element logarithm").
You can write ln in English too. Most mathematicians don't but calculators often have an "ln" button.
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July 9th, 2014, 05:04 PM   #15
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Monox--

Yeah, here in the US, when we write $\displaystyle \log\, x$, the base is automatically taken to be 10. When we write $\displaystyle \ln\, x$, the base is $\displaystyle e$.

As for $\displaystyle \mathbb{H}$ being used for the irrational numbers and $\displaystyle \mathbb{W}$ being used for the whole numbers, the only place I've seen these used is in a college textbook I use for teaching intermediate algebra: Intermediate Algebra, 5th Edition by Tussy and Gustafson.
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July 9th, 2014, 05:05 PM   #16
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Yeah, it's interesting-- if I remember, some books include 0 in the naturals, while others start them at 1. Does this have any major impact that you've seen?
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July 9th, 2014, 05:25 PM   #17
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You can write ln in English too. Most mathematicians don't but calculators often have an "ln" button.
So when you press normal "log" button the base will be 10?

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Monox--

Yeah, here in the US, when we write $\displaystyle \log\, x$, the base is automatically taken to be 10. When we write $\displaystyle \ln\, x$, the base is $\displaystyle e$.
Looks like you and CRGreathouse are also from different countries. Which country are you from, CRGreathouse?
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July 9th, 2014, 05:32 PM   #18
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Yeah, it's interesting-- if I remember, some books include 0 in the naturals, while others start them at 1. Does this have any major impact that you've seen?
The system here starts natural numbers at 1. However, there is some interesting note regarding the word "natural" here. "Natural numbers" here is called as "bilangan asli" which literally means "true numbers", though we still call "real numbers" as "bilangan real". While the literal translation of "natural numbers" in my language is "bilangan alam". However, the term "bilangan alam" in my language itself refers to "elementary numbers" e instead. This has made my very first post in this post very embarrassing because at the time I bumped a thread which said that "natural numbers" are 1, 2, 3, and so on only for me to say "Isn't natural number e?" in which one of the mods replied me with sarcasm "Best. Bump. Ever." and said that "natural numbers" were indeed 1, 2, 3, and so on. I was a smartass back then.
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July 9th, 2014, 09:03 PM   #19
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Which country are you from, CRGreathouse?
I'm in the US (though I did live in the UK for a few years).

Assuming that logs are base 10 is (sadly) common in grade school and even high school but fortunately pretty much stamped out by college.
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July 10th, 2014, 03:03 AM   #20
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Makes me wonder why they don't just write log2 and ln2 instead.
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