• Guest, we are doing a new map (refresh) for Herocraft. Gather your friends and get ready! Coming next Friday, 06/28/24 @ 7PM CT play.hc.to
    Read up on the guides and new systems! Here.
    View the LIVE Map here @ hc.to/map
    Stuck or have a problem? use "/pe create" to to open a ticket with staff (There are some known issues and other hotfixes we will be pushing asap)
  • Guest, Make sure to use our LAUNCHER! Read more here!

New Township Costs / Sizes

AlexDaParrot

AlexDaParrot

Legacy Supporter 5
Joined
Jan 12, 2011
jwplayer0 said:
I could actually explain how -1 = inf in math also.
Take the concept of 1+2+4+8+16... Doubling the number infinity times making it equal infinity.

Multiply that by 1 so it looks like (1)(1+2+4+8+16...)
then do 2-1 since that equals 1. (2-1)(1+2+4+8+16...)
Multiply that out then simplify. (2+4+8+16+32...)
___________________ (-1-2-4 -8 -16 -32...)

After simplifying the only thing your left with is -1 since everything else will cancel out with each other.

This makes infinity = -1
Click to expand...

Order of operations...PEMDAS

(2-1)(1+2+4....)
(2-1) = 1
1(1+2+4...) evaluated = inf
=Infinity

General Disproof

(A-B)(B+A+C+D+E...)
AB + A^2 + AC + AD +AE -B^2 - BA - BC -BD + BE
AB Cancels BA, but
A^2 + AC + AD + AE - B^2 - BC - BD + BE .... stays....
Because AE =/= BE [E = 16, B = 1, A=2] Thus AE = 32 and BE = 16.
Proof only works if A = B wherein the initial (A-B) = (A-A) or (0)
So (0) (......) = 0, not -1.
Also, because A > B, the quantity (A-B)(B+A+C+D+E....) Will never be less than 0.

If I missed something, it may just be that I failed to understand your logic, please, do correct me if I am looking at this incorrectly.
 
jwplayer0

jwplayer0

Legacy Supporter 6
Joined
Jan 14, 2011
Location
Columbus, OH
AlexDaParrot said:
Order of operations...PEMDAS

(2-1)(1+2+4....)
(2-1) = 1
1(1+2+4...) evaluated = inf
=Infinity

General Disproof

(A-B)(B+A+C+D+E...)
AB + A^2 + AC + AD +AE -B^2 - BA - BC -BD + BE
AB Cancels BA, but
A^2 + AC + AD + AE - B^2 - BC - BD + BE .... stays....
Because AE =/= BE [E = 16, B = 1, A=2] Thus AE = 32 and BE = 16.
Proof only works if A = B wherein the initial (A-B) = (A-A) or (0)
So (0) (......) = 0, not -1.
Also, because A > B, the quantity (A-B)(B+A+C+D+E....) Will never be less than 0.

If I missed something, it may just be that I failed to understand your logic, please, do correct me if I am looking at this incorrectly.
Click to expand...
Since im shit at explaining things, how about a video?
 
GreekCrackShot

GreekCrackShot

Legacy Supporter 7
Joined
Feb 1, 2011
Location
New York
I'm only confused at that equation because I don't see how 1, in 1+2+4+8+16... was cancelled... Maybe I'm just missing something, and I'm not that good at math, despite being in pre-calculus in sophomore year (would be better if my teacher didn't suck so bad)

But if you have
1+2+4+8+16... and multiply that buy 1, or 2-1, which is still 1, isn't it still 1+2+4+8+16...

then cancelling
1+2+4+8+16...
-1-2-4-8-16...

Then doesn't the -1 cancel too? Maybe this is just a concept I haven't got into, but no where in the process did he state how +1 just disappears into thin air.

Answer looks like 0
 
AlexDaParrot

AlexDaParrot

Legacy Supporter 5
Joined
Jan 12, 2011
jwplayer0 said:
Since im shit at explaining things, how about a video?
Click to expand...

(2-1) + (4-2) + (16-8) + (32-16)
You have to note that where x = 1 on the left side, X = 2 on the right side. So it may appear to be -1 after he put the -1 in the precarious place right before and tried to line them all up, but in actuality it continues to go to infinity. If you did just a limited number of sums as I did to illustrate how the rest of the continuum would go, you'd notice that the situation I outlined above [A^2 + AC + AD + AE - B^2 - BC - BD + BE ....] is true here as well.

A = 2
B = 1
2^2 + 2*4 + 2*8 + 2* 32 - 1^2 - 1*4 - 1*8 - 1*16
So 4 + 8 + 16 + 64 - 1 - 4 - 8 -16
Simplify (4+8+16+64) + (-1-4-8-16)
(92) + (-29)
= 63
As I said, his placement of the 1 just makes it appear to be an optical illusion. You approaching infinity in both series, but the one where it is multiplied by 2 is approaching it faster than the one that is multiplied by one [The subtraction one].

It may appear to make sense, but it is actually just a pseudo-proof that plays a misrepresentation of how the numbers of actually subtracted. Also, it is important to note that no matter how you multiply something by 1, you should always get the same answer out. If you fail to do so, the problem is going to be wrong in some way, as shown. Multiplying by one can be used to make the problem easier to solve, but not to change the answer itself.
 
Matt5327

Matt5327

Legacy Supporter 3
Joined
Apr 11, 2011
I'll give it a shot.

(1)(1+2+4+8…) =
(2-1)(1+2+4+8…)
True because of PEMDAS.

= (2)(1+2+4+8…)-(1)(1+2+4+8…)
True because of the distributive property.

= (2+4+8+16…)-(1+2+4+8…) =
(2+4+8+16…)+(-1 + -2 + -4 + -8…)
True because subtraction is adding a negative number by definition.

= (-1 + 2 + -2 + 4 + -4…)
True because of communitive property.

= -1
True because every number is canceled out except for -1. Even though one set may immediately appear to have another number the the second doesn't, it doesn't matter. Each set has infinity size, thus all numbers are canceled out, with the exception of -1.
 
AlexDaParrot

AlexDaParrot

Legacy Supporter 5
Joined
Jan 12, 2011
Matt5327 said:
I'll give it a shot.

(1)(1+2+4+8…) =
(2-1)(1+2+4+8…)
True because of PEMDAS.

= (2)(1+2+4+8…)-(1)(1+2+4+8…)
True because of the distributive property.

= (2+4+8+16…)-(1+2+4+8…) =
(2+4+8+16…)+(-1 + -2 + -4 + -8…)
True because subtraction is adding a negative number by definition.

= (-1 + 2 + -2 + 4 + -4…)
True because of communitive property.

= -1
True because every number is canceled out except for -1. Even though one set may immediately appear to have another number the the second doesn't, it doesn't matter. Each set has infinity size, thus all numbers are canceled out, with the exception of -1.
Click to expand...

You are getting infinity larger, not canceling numbers out. The answer to the equation is infinity. (2-1) + (4-2) + (8-4) + (16-8) +..... [The correct usage of the communitive property in this instance].

Because you are adding the (2-1), you are in fact doing the exercise 2A - A + 2B - B + 2C - C + 2D - D ... when utilizing the generic form of the equation, it is obvious that the numbers do not cancel out, but instead you are adding A + B + C +D
[2-1] [ A+ B + C +D]
[1] [A + B +C +D...]
I really find it preposterous that people are actually thinking that adding up an infinite series of POSITIVE integers somehow produces a negative number after some hand waving. This would be equal to saying 2 + 2 = -4.

While you could argue that it is -1 due to both quantities approaching infinity [2 Quantities going to +infinity and I am actually trying to sound as if it is logical for them to somehow appear at -1], the rate at which they approach infinity is different, and because infinity is not actually a number it can not be held as an "ultimate equalizer." In fact, the item must be evaluated forever, which would show that it is in fact approaching infinity because by pairing the terms as they appear you would get [2-1] + [4 -2] + [8-4] considering that you evaluate the function at n intervals at an indefinite amount of intervals, this process would be repeater forever, but the pattern of positively adding the numbers would still hold true.

I'd actually like to clarify that at the best case the equation would = Infinity - Infinity, which is definitely not -1. Infinity is not a concrete number, it is a concept.
 
You must log in or register to reply here.
Top