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Another Math Mind-bender  
User currently offlineRedngold From United States of America, joined Mar 2000, 6907 posts, RR: 45
Posted (13 years 10 months 5 days 2 hours ago) and read 887 times:

0.99999... = 1

Let x = 0.99999...
Therefore,
10x = 9.99999....

10x - x = 9x
Therefore,
9.99999... - 0.99999.... = 9

9x = 9
Therefore,
x = 1

That's the Algebraic conundrum.
If you want to know how to solve this seeming paradox, take Calculus!

redngold


Up, up and away!
5 replies: All unread, jump to last
 
User currently offlinePacific From Hong Kong, joined Mar 2000, 1051 posts, RR: 0
Reply 1, posted (13 years 10 months 5 days 1 hour ago) and read 711 times:

This is in the British curricilum for secondary 5 or 6. People taking GCSE maths have to learn it so I know how to do it!  

User currently offlineRedngold From United States of America, joined Mar 2000, 6907 posts, RR: 45
Reply 2, posted (13 years 10 months 4 days 23 hours ago) and read 707 times:

That's cool. But can you prove it correct or incorrect? We can see easily that algebra proves a seeming paradox. What does calculus have to say about this? One word: LIMITS!

redngold



Up, up and away!
User currently offlinePacific From Hong Kong, joined Mar 2000, 1051 posts, RR: 0
Reply 3, posted (13 years 10 months 4 days 22 hours ago) and read 705 times:

I've just started my British A-Level maths course in September so I've not learnt calculus yet! We don't do calculus in GCSE!

User currently offlineOxygen From Hong Kong, joined Sep 1999, 674 posts, RR: 1
Reply 4, posted (13 years 10 months 3 days 10 hours ago) and read 692 times:

x=0.999999999999999........= lim[x>1] x
10x-x
= 10 lim[x>1] x - lim[x>1]
= 9 lim[x>1]
= 9 (1)
= 9

So 9x Tends to 9.


User currently offlineFlyf15 From , joined Dec 1969, posts, RR:
Reply 5, posted (13 years 10 months 3 days 8 hours ago) and read 688 times:

I loved learning that back in Calc 1. Aren't limits fun?  

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