Jump to content
BrainDen.com - Brain Teasers
  • 0

An Associative fallacy


Go to solution Solved by bonanova,

Question

Consider the following sequence where

(1 + -1) + (1 + -1) + (1 + -1) + (1 + -1) + (1 + -1) + (1 + -1) ... now clearly this is the same as (0) + (0) + (0) + (0) + (0) + (0) ... = 0

however if I apply the associative property of addition to this series I get...

1 + (-1 + 1) + (-1 + 1) + (-1 + 1) + (-1 + 1) + (-1 + 1)  ... which clearly equals 1 + (0) + (0) + (0) + (0) + (0) ... = 1

But 1 does not 0, is the associative property wrong?

Link to post
Share on other sites

2 answers to this question

Recommended Posts

  • 0
  • Solution

Association holds for finite series. Infinite series converge only under certain conditions, which fail in this case. So it's not proper to give the series a value at all. But let's ignore that and call the series S anyway. Then what is S? Clearly it's 1/2:

Spoiler

   S = 1-1+1-1+1-1+1-...
0+ S = 0+1-1+1-1+1-1+1-...
--------------------------
0+2S = 1+0+0+0+0+0+... = 1

2S=1; S=1/2.

 

Link to post
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Answer this question...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
  • Recently Browsing   0 members

    No registered users viewing this page.

×
×
  • Create New...