0.9999999...... = 1

[Buzzer]

Right, if anyone out there is still somehow not convinced of the fact that they are equal, here is another proof, even more watertight:

1. You can write 0.99999999r = 0.9 + 0.09 + 0.009 + 0.0009....

Then using standard geometric summation (which unfortunately I can't use proper notation for in this, but imagine the symbols idf you will...)

Using a = 0.9, r = 0.1 we have

Sn = a + ar + ar^2 + ar^3 + .....
= a / (1-r)
=0.9 / (1-0.1)
=1




(Call me a geek all you want, but you can't say I'm wrong...)

Hang on a minute. This is at least 15 years ago I'm trying to remember this but isn't there a qualification that states

as n tends towards infinity Sn tends towards 1/(1-r)

rather than the blanket statement of Sn EQUALS 1/(1-r)?

Mathematicians, please help me here.

 

[Questions]

Racist.

He`s 0.99 of a racist I think you`ll find.

 

[Herr Tubthumper]

Hang on a minute. This is at least 15 years ago I'm trying to remember this but isn't there a qualification that states

as n tends towards infinity Sn tends towards 1/(1-r)

rather than the blanket statement of Sn EQUALS 1/(1-r)?

Mathematicians, please help me here.

Spot on, 1 is the limit. 1/(1-r) tends to one but never actually equals it.

 

[Lady Whistledown]

What happens at a petrol station, if you bought exactly one litre of petrol.

Would you have the right to expect to pay 89.9p, as advertised on the sign? Or demand to pay only 89p for it, as they can't provide the 0.1p change?

False advertising, I say.

 

[Buzzer]

What happens at a petrol station, if you bought exactly one litre of petrol.

Would you have the right to expect to pay 89.9p, as advertised on the sign? Or demand to pay only 89p for it, as they can't provide the 0.1p change?

False advertising, I say.

The advert is an invitation to treat in contract law. They are inviting you to make an offer of 89.9p per litre. You could make an offer lower than this or as is usual accept the invitation price for them to consider, accept or reply with a counter-offer. They could also, in their counter-offer, stipulate the amount that you could buy, say in units of ten litres only.

However, you do have a point as it could be construed in law that they are indicating their acceptance of whatever amount you so desire at the price of 89.9p by the very fact that they then provide you with the petrol that you want, not what they would necessarily want to sell you.

Their is a clear offer, acceptance and consideration on both sides.

You know what. I haven't the foggiest what the answer is.

 

[Rangdo]

here's Wikipedia's take on it. This article cites very reliable references.

I can't believe you're trying to back up your argument with a quote from Wikipedia. At least use a trustworthy source

 

[DTES]

Spot on, 1 is the limit. 1/(1-r) tends to one but never actually equals it.

1 is the limit, you are right.

And on the other side of the equation, 0.999999..... is the limit of 0.9 + 0.09 + 0.009 + 0.0009 + ........

That never reaches either. Both sides of the equation are limits. And the two limits are equal. That's the point.