## Welcome to BrainDen.com - Brain Teasers Forum

 Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-)
Guest Message by DevFuse

# All the people like us are We, and everyone else is They.

16 replies to this topic

### #1 bonanova

bonanova

bonanova

• Moderator
• 6160 posts
• Gender:Male
• Location:New York

Posted 05 July 2012 - 06:50 AM

Title is fav quote by Kipling, on equality.

How about you on the same subject, but mathematically, not philosophically:

Can two numbers x and y written in decimal expansion differ in every decimal place, yet be equal?
• 0

Vidi vici veni.

### #2 ujjagrawal

ujjagrawal

Junior Member

• Members
• 67 posts
• Gender:Male
• Location:India

Posted 05 July 2012 - 07:44 AM

Spoiler for how about it ?

• 0

### #3 envy

envy

Newbie

• Members
• 1 posts

Posted 05 July 2012 - 09:24 AM

0.999......
1.000...... are not "almost equal" ... they are EQUAL
proof 1)) 1/3 = 0.333......
3*1/3 = 0.333*3 but also 3*1/3 = 1
0.999.... = 1
proof 2)) let x = 0.999.....
10x = 9.999....
subtract the two equations.... 9x = 9 ... or x=1, but assumption 1, x=0.9999 ..... thus 0.999.... = 1 ....or if you like, 1.0000.....
• 2

### #4 ujjagrawal

ujjagrawal

Junior Member

• Members
• 67 posts
• Gender:Male
• Location:India

Posted 05 July 2012 - 10:13 AM

• 0

### #5 witzar

witzar

• Members
• 233 posts

Posted 05 July 2012 - 12:47 PM

the difference may be infinitesimally small but it exists...

1. The difference of two real numbers numbers always exists and is also a real number.
2. A real number cannot be "infinitesimally small".
3. Please don't answer "thanks for the explanation, but I'll stick to... "
• 1

### #6 dpalmer

dpalmer

Newbie

• Members
• 7 posts

Posted 05 July 2012 - 03:17 PM

Spoiler for Got one

• 1

### #7 bonanova

bonanova

bonanova

• Moderator
• 6160 posts
• Gender:Male
• Location:New York

Posted 05 July 2012 - 03:24 PM

1. The difference of two real numbers numbers always exists and is also a real number.
2. A real number cannot be "infinitesimally small".
3. Please don't answer "thanks for the explanation, but I'll stick to... "

To what class of numbers do those that are infinitesimally small belong?
• 0

Vidi vici veni.

### #8 jim

jim

Junior Member

• Members
• 33 posts

Posted 05 July 2012 - 03:34 PM

In standard mathematics 1.000... and 0.999... are considered to be two different ways to express exactly the same number.
• 0

### #9 bonanova

bonanova

bonanova

• Moderator
• 6160 posts
• Gender:Male
• Location:New York

Posted 05 July 2012 - 03:38 PM

Spoiler for how about it ?

Spoiler for a discussion of almost

• 0

Vidi vici veni.

### #10 jim

jim

Junior Member

• Members
• 33 posts

Posted 05 July 2012 - 03:39 PM

There are infiniesinally small real numbers in the non-standard real number system of Abraham Robinson which he used in his non-standard analysis. That system allows a form of calculus where the derivative is the ratio of two infinitesimals.
• 0

#### 0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users