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16 replies to this topic

#1 bonanova

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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?
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#2 ujjagrawal

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Posted 05 July 2012 - 07:44 AM

Spoiler for how about it ?

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#3 envy

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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.....
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#4 ujjagrawal

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Posted 05 July 2012 - 10:13 AM

Spoiler for Please use spoilers

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#5 witzar

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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... " :)
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#6 dpalmer

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Posted 05 July 2012 - 03:17 PM

Spoiler for Got one

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#7 bonanova

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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?
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#8 jim

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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.
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#9 bonanova

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Posted 05 July 2012 - 03:38 PM

Spoiler for how about it ?


Spoiler for a discussion of almost

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#10 jim

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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.
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