Endless Paradigm

To understand this post you need a certain amount of maths knowledge and/or a TI84+ calculator. I'd recommend both.

The complex number i is defined as the square root of (-1).

When you raise i to powers, there is a pattern:

i^0 = 1

i^1 = √-1
i^2 = -1
i^3 = -1√-1
i^4 = 1

i^5 = √-1
i^6 = -1
i^7 = -1√-1
i^8 = 1

i^9 = √-1
i^10 = -1
i^11 = -1√-1
i^12 = 1

etc.
As you can see and calculate, any power of i that is a multiple of four is 1, because any even power eliminates the complex part and -1 * -1 = 1.

However, on the TI83/84, try typing i^4. Good. Now try i^8. Lolwut??? Same goes for i^12.

Lets do it by hand:

i^8 = i^(2^4)
i ^ 2 = √-1 * √-1 = -1
(-1)^4 (even on your calculator) = 1. So why isn't it one on the TI??


Another lie:

Take a very small number, e.g. 0.0000000000001 (1x10^-13)

Type it into your calc. It'll probably say either the same number again or 1E-13, which is the same but in scientific notation.

Now let's just get one very simple thing straight. Imagine any number x. Add one to get x + 1. Now substract one. You get x, right? So x + 1 - 1 = x, yeah? That's so simple, its unbelievable a calculator can't even do it! Try this: type 0.0000000000001 + 1 - 1.

Now you will never trust your calculator again.

That is some weird sh!t. I never liked calculators much anyhow. . . . .fvcking liars!!!

Calculators For the loss

Even things like M$ Excel cannot add up 77.1*850

1+1= " I hope future super computers don't have a hard time with this one"

LIARS ALL LIARS!

UncertainGod Wrote:Calculators For the loss

Even things like M$ Excel cannot add up 77.1*850

O_o



Though the other things is probably due to floating point notation.  It's known that a computer will "round" a very precise decimal to the nearest floating point representation, ie, to a computer (using single/double precision floating point) 0.999999999999999999999 = 1.

Looks like its back to the abacus...

ZiNgA BuRgA Wrote:

UncertainGod Wrote:Calculators For the loss

Even things like M$ Excel cannot add up 77.1*850

O_o



Though the other things is probably due to floating point notation.  It's known that a computer will "round" a very precise decimal to the nearest floating point representation, ie, to a computer (using single/double precision floating point) 0.999999999999999999999 = 1.

according to my source for the second part (the first part i found out myself), the ti supports up to 14 decimal places. so 0.0000000000002 / 2 does amount to 0.0000000000001 but if you add and substract a large number, then it will set it to 0 incorrectly. this is to prevent calculations with fractions to get answers like 3.000000000000001 when its actually 3 in real life, so basicly ye its a flaw in the calculator, not a rounding error.

Ge64 Wrote:according to my source for the second part (the first part i found out myself), the ti supports up to 14 decimal places.

"Support" doesn't necessarily mean accurate - If I recall correctly, double precision floating points can "support" up to around a few hundred decimal places - obviously, an 8 byte number can't represent all those accurately..

Ge64 Wrote:so 0.0000000000002 / 2 does amount to 0.0000000000001

0.0000000000002 can be fully represented in single precision floating point:
0.0000000000002 = 0x2A612E13
See if you get the expected result if you do this:
0.9999999999 / 2 = ???

Ge64 Wrote:but if you add and substract a large number, then it will set it to 0 incorrectly. this is to prevent calculations with fractions to get answers like 3.000000000000001 when its actually 3 in real life, so basicly ye its a flaw in the calculator, not a rounding error.

It's because there is no representation for 3.000000000000001 in single or double precision floating point - the closest thing there is to 3.000000000000001 is 3.