Cheat Engine

DanielG · Posted: Fri Jun 19, 2009 3:06 pm Post subject:

In mathematics, the repeating decimal 0.999… denotes a real number equal to one.
In other words: the notations 0.999… and 1 actually represent the same real number.
This equality has long been accepted by professional mathematicians and taught in textbooks.
Proofs have been formulated with varying degrees of mathematical rigour, taking into account preferred development of the real numbers, background assumptions, historical context, and target audience.

Everyone who says 0.999... does not equal one hasn't gone beond basic high school math and doesn't understand the concept of infinity.

"The students' reasoning for denying or affirming the equality is typically based on one of a few common erroneous intuitions about the real numbers; for example that each real number has a unique decimal expansion, that nonzero infinitesimal real numbers should exist, or that the expansion of 0.999… eventually terminates. Number systems that bear out some of these intuitions can be constructed, but only outside the standard real number system used in elementary, and most higher, mathematics. Indeed, some settings contain numbers that are "just shy" of 1; these are generally unrelated to 0.999…, but they are of considerable interest in mathematical analysis."

"Students of mathematics often reject the equality of 0.999… and 1, for reasons ranging from their disparate appearance to deep misgivings over the limit concept and disagreements over the nature of infinitesimals. There are many common contributing factors to the confusion:

* Students are often "mentally committed to the notion that a number can be represented in one and only one way by a decimal." Seeing two manifestly different decimals representing the same number appears to be a paradox, which is amplified by the appearance of the seemingly well-understood number 1.
* Some students interpret "0.999…" (or similar notation) as a large but finite string of 9s, possibly with a variable, unspecified length. If they accept an infinite string of nines, they may still expect a last 9 "at infinity".
* Intuition and ambiguous teaching lead students to think of the limit of a sequence as a kind of infinite process rather than a fixed value, since a sequence need not reach its limit. Where students accept the difference between a sequence of numbers and its limit, they might read "0.999…" as meaning the sequence rather than its limit.
* Some students regard 0.999… as having a fixed value which is less than 1 by an infinitesimal but non-zero amount.

These ideas are mistaken in the context of the standard real numbers, although some may be valid in other number systems, either invented for their general mathematical utility or as instructive counterexamples to better understand 0.999…."

yes largly quoted from wikipedia

oib111 · Posted: Fri Jun 19, 2009 3:13 pm Post subject:

First off, if you can prove to me mathematically that .99999.... and 1 are not the same, please do, otherwise refrain from speaking.

SF · Posted: Fri Jun 19, 2009 3:18 pm Post subject:

Right, and the oh so smart math people said that .999... is equal to 1 to make shit easier, when in reality it is not the same number. No, you can't stick a number between it...but does this mean that 5.99999... is equal to 6? No, but for ease of solving crap it does. You can throw out your explanations for how .999... is the same as 1 all you want, but as you can see on your screen, they are not the same number. We all choose to accept that they are to make our lives easier.

Okay...since some of you still don't see where I'm coming from...

0.999... != 1, the only reason people say it does is to make things easier (since you can't use an infinite number in math problems) This is rounding, that is all it is and that is all it will ever be.

zyndr0m · Posted: Fri Jun 19, 2009 3:34 pm Post subject:

Thats like saying PI is exactly 3.14.

Slugsnack · Posted: Fri Jun 19, 2009 3:35 pm Post subject:

no.. omg they are EQUAL. of course it's not the same number.

if you say :

a = b

a is LOGICALLY EQUIVALENT to b but they are different. if you think they're the same you need to get your eyes checked out. this is a fundamental that is learnt when you learn logic

but 0.9... recurring IS EQUAL AND LOGICALLY EQUIVALENT. no they are not the same number but they hold THE SAME VALUE it's not about accepting that they are the same.. read the proofs and you will find they ARE the same. the one i posted on the last page is easiest to accept IMO

both of you should read the thing properly before commenting next time..

Monkeys · Posted: Fri Jun 19, 2009 3:39 pm Post subject:

zyndr0m · Posted: Fri Jun 19, 2009 3:39 pm Post subject:

3/3 is supposed to be 1, but it can never be one whole because 1/3 is infinite and so is 2/3.

@monkey what?

Slugsnack · Posted: Fri Jun 19, 2009 3:55 pm Post subject:

x = 0.333......

10x = 3.3333....

10x - x = 3.3333... - 0.33333...

since both recur forever we can safely 'cancel' out both decimal parts :

9x = 3
3x = 1

since apparently you failed to read my first post in this topic..

zyndr0m · Posted: Fri Jun 19, 2009 4:04 pm Post subject:

Slugsnack · Posted: Fri Jun 19, 2009 4:08 pm Post subject:

are you blind ? when did i round anything ?! the ......s represent that that number continues to infinite

i don't see why this is such a hard concept for you to grasp..

point out which exact line you did not understand..

zyndr0m · Posted: Fri Jun 19, 2009 4:10 pm Post subject:

Monkeys · Posted: Fri Jun 19, 2009 4:12 pm Post subject:

Slugsnack · Posted: Fri Jun 19, 2009 4:16 pm Post subject:

okay.. if 1.33333... << RECURRING TO INFINITE and subtract 0.3333 << RECURRING INFINITE. then we can see it as :

1 + 0.3333333..... - 0.333333.....

since the two second parts are equal.. then yes you can 'cancel it out'

never mind, giving up you guys will learn basic maths when you hit the age of 15

Monkeys · Posted: Fri Jun 19, 2009 4:18 pm Post subject:

zyndr0m · Posted: Fri Jun 19, 2009 4:20 pm Post subject: