Air

Hello All! I'm 'Air'. Like Mathematics (hence most likely to be seen in the Mathematics forum) and hence have an occupation of studying it. I hope to be active member of the forum and contribute to threads. See you around.

The reactivity of an atom is determine by the vacancy (unfilled orbital) in the outermost shell of an atom. Greater vacancy implies greater reactivity (and vice versa).

If zero's are recurring, at which point would you be able to attach a zero at the end?

Hmmm... Not quite. I was just posting an alternative proof. This thread is about (Quoted OP):

An alternative approach (using fractions): [math]\frac13 = 0.33333...[/math] [math]\frac13 \times 3 = (0.33333...) \times 3[/math] [math]1 = 0.99999...[/math]

Yes, normally you are told that you get the result 1 if you divide a number by itself. If you permit this result at [math]\frac{0}{0}=1[/math] then the value of all numbers isn't unique anymore. An example: [math]5 \cdot 0 = 9 \cdot 0[/math]. Now divide both sides of this equation by zero: [math]\frac{5 \cdot 0}{0} = \frac{9 \cdot 0}{0}[/math]. According to the assumption you can cancel out the zeros and you'll get [math]5 \cdot 1= 9\cdot 1[/math]. Does 5 equal 9? Do you now see why zero is a special case? [math]\lim_{x \to 0^+} \ \frac 1x=+ \infty[/math] [math]\lim_{x \to 0^-} \ \frac 1x=- \infty[/math] [math]\lim_{x \to +\infty} \ \frac 1x=\lim_{x \to -\infty} \ \frac 1x=0[/math] [math]\frac{\text{Number}}{0}[/math] is undefined [math]\left(\frac{0}{0} \ne \frac{1}{\infty}\right)[/math]. It is different from the limit.

When you rearrange the formula, you are able to get it into the form [math]ax^2 + bx + c =0[/math]. [math]s = {v_0}t + \frac{1}{2}at^2 \rightarrow \frac12 at^2 + {v_0}t - s = 0[/math]. This implies: [math]a = \left(\frac12 a\right), \ b={v_0}, \ c={-s}[/math]. For these type of formula, known as the quadratic equation (Highest power is 2), you can use the quadratic equation to find the value of [math]x[/math]. The quadratic formula is: [math]x= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/math]

He is best known for his theory of relativity and specifically mass–energy equivalence, [math]E = mc^2[/math]. Einstein received the 1921 Nobel Prize in Physics "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect". SOURCE: http://en.wikipedia.org/wiki/Albert_Einstein

I like Euler's Identity too, [math]e^{\pi i} + 1 = 0[/math]. It's one of those equations which would strike people's mind when we say 'Mathematics' just as when we say 'Physics', people's mind will get Einstein's equation [math]e=mc^2[/math].