i saw an equation in my dreams lastnight! opinions?

[ladybug77]

Let's say I wish to walk from the spot I am standing 5 feet forward. I do. I am now five feet from where I began. If I walk 7 feet in the opposite direction, I can represent this on the number line like so:

-4__-3__-2__-1__0__1__2__3__4__5__6

I started at 0 and walked five feet forward. Now I take away 7 by walking backwards.
-4__-3__-2__-1__ 0__1__2__3__4__5__6

I don't end up one foot behind where I started. I end up 2 feet behind where I started. I note this by placing a " - " sign to indicate that I have ended up behind where I started. Mathematics is all about precision. I can add apples and oranges if I say that 4 oranges plus 5 apples is equal to 9 pieces of fruit because I am actually not adding oranges or apples but pieces of fruit. What I can't do is say I have 9 apples.

You started at 1. You took 5 feet forward. Your at 6. Take 7 steps back, your at -2.
Still 2 steps away from where you started. Just the zero doesnt belong. You atarted at somewhere. Not nowhere.

 

[Kilgore Trout]

Again, what is -1/2 + 1 = in your system?

 

[Curious George]

5+(-7)=-2 thats the old way. The wrong way.

5+(-7)=-1 thats correct.

I think you mean 5+(-7)=-3 in your system. Pull out your adjusted number line.

 

[Curious George]

You started at 1. You took 5 feet forward. Your at 6. Take 7 steps back, your at -2.
Still 2 steps away from where you started. Just the zero doesnt belong. You atarted at somewhere. Not nowhere.

No in your number line he started at -1, not 1. He didn't have a step before he took a step.

 

[Willamena]

Ah, I missed the correction. 1 -1 is the handoff, and -1 +1 is the handback. What we've devised is a symbolic language for item exchange. I'm liking this thead more and more.

 

[ladybug77]

So does this then mean that 5*-1= -1 and 5*-2=-5?

What about 1*-2 this would be -1 or -2?

And -2*-2=2(not 4) but -1*-1=-1?

Further, 3^-1=1 and 3^-2=1/3 but -(1^x)=-2?

I just think your system causes unnecessary confusion.

Further you are saying that if you owe me 3 dollars and pay me two then your balance is -2.

Also 3/1=3 and -(3/1)= -4. but -3/-2=2 yet (-2) (3)/(-2) (2)= 3/2.

Sorry your system does not work.

1-2 is -2.
-2-2 is -4.

If i owed you 3 dollars, and i gave you two. Its simple.
Im -3 owing you. I give you 2. Now im -1 owing you.
My balance is -1.

Its not flawed.

 

[ladybug77]

No in your number line he started at -1, not 1. He didn't have a step before he took a step.

Either way...he took the same amount of steps, and ended up the same amount of steps away from the starting point. But zero doesnt belong there.

 

[ladybug77]

I think you mean 5+(-7)=-3 in your system. Pull out your adjusted number line.

Yea, youre right. Its -3.

 

[Curious George]

1-2 is -2.
-2-2 is -4.

If i owed you 3 dollars, and i gave you two. Its simple.
Im -3 owing you. I give you 2. Now im -1 owing you.
My balance is -1.

Its not flawed.

It absolutely is. if your balance is -1 then when you pay that last dollar you have to be at +1 dollars. Now you created an extra dollar.

 

[LegionOnomaMoi]

You started at 1.

I didn't. Because I am only interested in the number of feet I have travelled in a particular direction. I don't start having travelled 1 foot. That's why it is important to say what the numbers and operations are corresponding to. If I am interested in how many feet I move from a particular spot, and I move first 5 feet forward and then 7 feet back (5 + -7) then I have moved 2 feet from the spot I started from. In order for this to work I pick an origin point I call 0. If you wish to measure a length of 50 centimeters on a table, you don't do this by starting at one centimeter. You start at zero and measure out 50 centimeters.

You took 5 feet forward. Your at 6. Take 7 steps back, your at -2.

If this were true, then I started out one foot forward. I didn't start out one foot forward.

You started at somewhere. Not nowhere.

0 doesn't mean nowhere. In order to find out how many feet, miles, kilometers, etc., I travel, I pick a place to start counting from. That place is 0. It need not be. If I am in business, I may start out in debt. I would probably represent that debt by a negative amount of say -700 dollars. If I then earn 700 dollars and pay my debt I am not where I started but I am at 0. What matters is what I am saying the operations and numbers correspond to. If I'm doing quantum mechanics I'm using complex numbers in Hilbert space. If I'm doing relativistic physics or measuring distances in 1000-dimensional space for statistical analysis I may not even use standard (Euclidean) geometry. There is no particular reason for the order of operations used in basic calculus or algebra. There is a need for such an order, because if I have something like
80 + 30/2
I need to know which operation to do first as depending upon which I choose I will get different answers.

 

[ladybug77]

Again, what is -1/2 + 1 = in your system?

Sorry it got overlooked: i gotta think that threw. Not sure yet. I was always horrible at fractions.

 

[Willamena]

0 doesn't mean nowhere. In order to find out how many feet, miles, kilometers, etc., I travel, I pick a place to start counting from.

ladybug, zero is a placeholder. This, what Legion explained, is what use the placeholder serves.

1 is taking one step forward, and -1 is taking one step back. Neither is the starting point.

(Although it would be really cool to start a journey twenty steps behind yourself.)

 

[Kilgore Trout]

Sorry it got overlooked: i gotta think that threw. Not sure yet. I was always horrible at fractions.

Well, let's make it easier - what would 1/2 + 1 be?

 

[Curious George]

Yea, youre right. Its -3.

You are eliminating 0. for most math this does not matter, as we can rename numbers any way we choose. The problem stems from bringing the negative sign. You need to have a neutral separation between positive, and negative. If -1 become the new zero that is fine but a problem occurs when you try to extend the negative sign as if it has importance. In your system -(1) = -2(1) opposed to -1(1). This doesn't effect to much beyond making the system more confusing, but it creates order of operation problems that become huge problems with more complex math.

 

[Poeticus]

They make fun it, and have yet to challenge it. Its sad.

It's so bafflingly hopeless of a situation that it's horridly unapproachable because it does not make reasonable sense.

 

[Kilgore Trout]

Well, let's make it easier - what would 1/2 + 1 be?

Let's make it even easier: Where does 1/2 fall on your imaginary number line? Where does -1/2 fall?

 

[ladybug77]

It absolutely is. if your balance is -1 then when you pay that last dollar you have to be at +1 dollars. Now you created an extra dollar.

Nope. I owe you a dollar. Im -1 in the hole.
When i recieved the dollar...im +1.
When i give it to you im -1 again. I did not create anything extra.

 

[Jainarayan]

Either way...he took the same amount of steps, and ended up the same amount of steps away from the starting point. But zero doesnt belong there.

Standing at his starting point, how many steps did he take? What number of steps is standing represented by? This is relative to our example of motion and numbers quantifying motion.

 

[Curious George]

It's so bafflingly hopeless of a situation that it's horridly unapproachable because it does not make sense; in fact, it defies mathematical sense.

You are basically perverting the natural number line by taking out 0 to justify your fabricated, imagined, fantasy boloney.

If you were to take your new found, dreamed "revelation" to a nearby university, they would laugh at you and most likely suffer a wrongful stroke from the laughter due to such high levels of stupidity that it would be mind-boggling.

This whole thread has evaporated, dissipated, fizzled any credibility as a sane person you previously may have had.

If you have children, I worry about their future. No, really. I seriously, seriously do. In fact, this whole thread qualifies you for a psych eval - heck, even an emergency petition will do.

In all my time on RF, I have seen some dumb things. But, congrats: you are the creme de la creme.

I would really like to give you a negative frubal. Not only were your above comments
Unnecessary, but they were also mean and run contrary to the spirit of RF.

 

[ladybug77]

Let's make it even easier: Where does 1/2 fall on your imaginary number line? Where does -1/2 fall?

The half falls in between all whole numbers.

Ok. If im at -1/2, and i recieve one whole. I have a whole. Its 1.

In senerio though, if i owed you half of a dollar...and i made one dollar. I have that one dollar. Its until i pay you the 1/2 that i end up with 1/2 a whole.