Jump to content

Recommended Posts

I've added support for typesetting math using LaTeX on the forums.

 

Example:

[tex]\sum_{n = 0}^\infty \frac{1}{n!} = \lim_{n\to\infty} \left(1+\frac{1}{n}\right)^n = e[/tex]

 

Outputs:

[tex]\sum_{n = 0}^\infty \frac{1}{n!} = \lim_{n\to\infty} \left(1+\frac{1}{n}\right)^n = e[/tex]

 

Just in case anyone wanted to write some math that's a little more advanced than basic arithmetic.

 

Update:

 

The [tex] bbcode is now deprecated in favor of [math] and [imath]. The former is used for display mode, the latter is for inline mode.

 

Example of display mode:

[math]\sum_{n = 0}^\infty \frac{1}{n!} = \lim_{n\to\infty} \left(1+\frac{1}{n}\right)^n = e[/math]

 

Inline mode is used for math in sentences, like you might want to say [imath]\frac{1+2}{5}\cdot7=\frac{21}{5}[/imath] within a sentence.

Link to comment
https://forums.phpfreaks.com/topic/140190-typing-math/
Share on other sites

Well... the definition is [tex]x^2 =  -1[/tex]

 

Saying that [tex] i  = \sqrt{-1}[/tex] is not incorrect as long as you make it clear, that [tex] \sqrt[/tex] operator is redefined here as compared to the one used for real numbers.

 

[tex]\sqrt{-x} = i \sqrt x[/tex] where [tex]0 < x \in \mathbb{R} [/tex]

 

 

Link to comment
https://forums.phpfreaks.com/topic/140190-typing-math/#findComment-734952
Share on other sites

[tex]x^n = y \Leftrightarrow \sqrt[n]{x^n} = x = \sqrt[n]{y}[/tex], no?

 

It's because [tex]\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}[/tex] is only true for [tex]a \in \Bbb{R}^+ \cup \{0\}[/tex] and [tex]b \in \Bbb{R}^+ \cup \{0\}[/tex] or something like that. That's the "trick" or whatever... There is another "proof" that says that any integer a equals any other integer b, I just can't remember that one, but there is of course an error in that one as well.

Link to comment
https://forums.phpfreaks.com/topic/140190-typing-math/#findComment-734958
Share on other sites

  • 1 month later...
  • 2 months later...

Actually corbin, it's widely accepted among mathematicians that .999... = 1. ShadeSlayer's proof may be said to be flawed in the sense that it doesn't explain how the pattern he uses works.

 

A better version might be:

[tex]\frac{1}{3} = 0.\overline{333}[/tex]

[tex]3 \cdot 0.\overline{333} = 3 \cdot \frac{1}{3} = \frac{3}{3} = 1[/tex]

 

Therefore:

[tex]0.\overline{999} = 1[/tex]

Link to comment
https://forums.phpfreaks.com/topic/140190-typing-math/#findComment-830823
Share on other sites

Dunno if it helps your understanding, but 0.99 is closer to 1 than 0.9 is, so for each 9 you add, you get closer to 1. If you have an infinite amount of 9's then you are getting infinitely close to 1. Or if you want it in math terms:

 

[tex].9 = \frac{9}{10^1}[/tex]

[tex].09 = \frac{9}{10^2}[/tex]

[tex].009 = \frac{9}{10^3}[/tex]

etc.

 

[tex].9 + .09 + .009 = \frac{9}{10^1} + \frac{9}{10^2} + \frac{9}{10^3} = .999[/tex]

 

So:

[tex]\sum_{n=1}^{\infty} \frac{9}{10^n} = 0.\overline{999} = 1[/tex]

 

You see that as [tex]n \to \infty[/tex] (analogous to "you are adding more 9's on the end") you are getting closer to 1.

Link to comment
https://forums.phpfreaks.com/topic/140190-typing-math/#findComment-831082
Share on other sites

Yeah, we actually discussed this in class one day when talking about geometric sequences a while back.

 

 

And yes, as n -> inf., the number gets closer to 1, but it would never actually reach one.

 

 

Wouldn't .999 (repeating) = 1 - 1/inf, not 1?

 

 

 

(I do realize that obviously I'm arguing pointlessly since people accept .999 to be 1, just like .333 is assumed to be 1/3 [both repeating].  I guess  I just think that things should be left in fractional form ;p.)

Link to comment
https://forums.phpfreaks.com/topic/140190-typing-math/#findComment-831085
Share on other sites

This thread is more than a year old. Please don't revive it unless you have something important to add.

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Restore formatting

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.