Mathematics/Trivia: Difference between revisions

* [[wikipedia:0.999|0.999...]], which is a decimal with an infinite number of nines behind it, is ''exactly'' equal to 1. Not almost, not "so close there's no practical difference," ''exactly equal''. Here are three proofs of this:

** First, from the accepted decimal expansions of some fractions, such as:

1{{=}}0.999... }}

** Second, by simple algebraic manipulation:

1 {{=}} x }}

** Third: implicitly, 0.999... represents an infinite geometric sum of its digits, 9/10 + 9/100 + 9/1000 + ..., for which we can use the standard formula for the sum of a geometric series<ref>which, incidentally, is proven using a construction similar to the second proof</ref>:

{{=}} 9 * (1/10)/(1 - 1/10) {{=}} 9 * 1/(10-1) {{=}} 9 * 1/9 {{=}} 1 }}

 

* [[wikipedia:New Math|New Math]]. Yes folks, the brilliant folks in charge of our education systems tried to throw matrix ops, set theory, number bases, and abstract algebra at [[There Is No Kill Like Overkill|elementary schoolers]]. Many of the elementary teachers ordered to do the throwing didn't know the material themselves and wouldn't have been able to teach it to high school and college students of appropriate level and background.

** I believe that our [[Viewers Are Geniuses|youth can handle this!]]

''and you take away 3 and leaves... 9''! }}

 

* Here's a fun one to amuse your friends: 111111111 X 111111111 = 12345678987654321

* So you need to find the square root of a number, but you have one of those cheap calculators that don't have a square root function, or maybe you don't have a calculator. No worries, there's a quick, simple and Babylonian way to solve this problem.

4) The final G is the square root of N. }}

** Example: What is √65536<ref>Programmers, don't blurt out the answer</ref>? (Uh... I don't know, 376?)

Therefore, √65536 {{=}} 256 }}

** Fun fact: If your initial guess is a negative number, you'll get the negative root as the answer. That is, if the initial guess for √65536 was -376, the final answer would have been -256.