peterpqa wrote:
** Edit: **There is also a mathematical "proof" that 0.99999... is equal to 1, which it is not. |

I am very sorry but you are displaying your ignorance. 0.999999 ... is equal to 1

wherethe digits go to infinity. Remember it is often better to remain silent, and let people think you are stupid; than speak, and remove all doubt.

Just because you do not understand something does not mean it is wrong.You either have to educate yourself to the level at which you understand these things; or you have to trust the people who have so educated themselves, and who therefore know more than you know. You trust your doctor, your brain surgeon, you trust the engineer who designed your phone and your car. Every time you use the internet to buy something you trust the mathematicians who designed the cryptography making the transaction secure. You trust your GPS but you undoubtedly have no idea of Einstein's General Theory of Relativity, the Sagnac Effect, or the change in the rate at which time passes (time dilation) due to the satellite's speed and the change in the rate at which time passes due to gravitational potential. Fortunately

Neil Ashby and his colleagues did understand all these and incorporated them into the GPS system design, which is why GPS works. Learn to trust those who know more than you.

Nobel Prize winner Feynman famously had "If I cannot prove it, I don't understand it" at the top of his office blackboard. Take a lesson from him.

The best skill you can acquire is the judgement to choose who to trust, and not to say "I don't understand it so it must be wrong".

The proof that 0.999999 ... is equal to 1

where the digits go to infinity is so extremely simple - just 2 lines - that I hope you will be able to understand it.

Line 1. 1/9 = 0.1111111 ..., where the digits go to infinity.

Agreed?Now, you can multiply both sides of the equation by 9.

Agreed? Let's do so.

Line 2: 1 = 0.9999999 ..., where the digits go to infinity.

Therefore you

must agree that 0.9999999 ..., where the digits go to infinity, is equal to 1.

QED

Note that I can

tell you this proof, but I cannot

understand this proof for you - you have to understand it for yourself.

Can I suggest you read Georg Cantor on infinities (infinities come in different sizes). He also explains why irrational numbers cannot be expressed as ratios of integers. The fact that 0.99999... is equal to 1 is an essential part of Cantor's Diagonal, and hence Goedel's Incompleteness Theorems.

The next time you see something you think is wrong (like pi can be expressed as a fraction, or 0.999999... = 1) you really need to prove that it is wrong before you criticise it. If you cannot prove that something you think is wrong actually is wrong, then do not say that it is wrong.