rep'nA wrote:"....What is it they say? "We give an inch and you'll take

.999... miles".

Quite clever

Bigtone53 wrote:"..but the concept of infinity is a difficult one to grasp..."

I agree and this is probably why I'm finding it difficult to accept that .99999(repeating) will eventually equal 1.

Bigtone53 wrote:"2. .... By writing down the numbers 0.9, 0.99, 0.999 etc, you are generating a series of individual numbers on the line which will approach (ie get as near to as you wish ) the real number that is 0.999... , but will never quite get there. No member of this series will equal 0.999 ... and hence no member of the series will equal 1...."

Even accepting that the real number for .999... is 1, the above statement implies (to me anyway) that no matter how far you write down the numbers 0.9, 0.99, 0.999 etc. to get

as near to this "imaginary" real number 1 you will still never quite get there.

rep'nA wrote:"... Every term in the sequence .9, .99, .999, .9999,... has a finite number of 9's and so each term is less than 1. But as .999... has an infinite number of 9's, each term in the sequence is also less that .999... This doesn't show that .999... = 1, but it does show that your sequence of numbers isn't the same as .999... either. ..."

True but I would think it's somewhere between .999... and 1 and therefore still never reaches 1.

It looks like we still have different views on this and I again thank you for your patience. Browsing quickly through all the posts again I found it hard to dispute the logic of the following two particular posts which presented good arguments why .99999(repeating) =1.

wapati wrote:One third plus one third plus one third = 1, exactly.

.333 repeating plus .333 repeating plus .333 repeating = .999 repeating,

which is one.

udosuk wrote:Let x=0.999999...

10x=9.999999...

9x=10x-x=9.999999...-0.999999...=9

Therefore x=1.

(Q.E.D.)

I've been persistently arguing that .99999 (repeating) doesn't equal 1 but now I'm not sure

Cec