0.9999... = 1

Pretty funny thread on 2+2. Somebody posted a poll: Does 0.999... = 1?

It is funny because 0.99999... (where "..." means infinite more 9s) is equal to 1. But several people vehemently disagree about this mathematical fact.

Some of my favorites:

A.

You can show (using calculus or other methods) that with a large
enough number of 9s in the expansion, you can get arbitrarily close to
1.

SO in Math it does = 1 , however in reality it doesn't but its accepted that it is. So is the accepted answer its 1 , then yes, is it really no.

B.

They are not equal except in practical terms. It is similar to the question if I travel half the distance to my destination, then half again, on adinfinitum, will I ever reach my destination - no.

C.

I doesn't matter how many 9's there are in the .99999. The number you end up with is still some tiny tiny amount less than 1. That should be obvious but sadly looking at the results of the poll it isn't.

The guy in quote A is willing to draw a line between "math" and "reality." In other words "I don't care what all the experts who understand this issue say, my ignorant opinion is going to govern my reality."

The guy in quote B might have just proved to himself that he can never actually reach any destination.

The guy in quote C is so confident that his wrong answer is right that he actually looks down on people that understand the right answer to the question.

People's confusion on this matter stems from a flawed understanding of the decimal system, difficulty with the concept of infinity and poor math education. They cling to their sense of intuition which is good for concepts like 1, 2, or 10, but is woefully lacking when dealing with complex concepts like infinity. They even dismiss examples that appeal to intuition, like 1/3 = 0.333..., so 3/3 = 0.9999... = 1. Each intuitive step leads to an counterintuitive conclusion, so they ignore it.

Sometimes when people disagree, there is no right answer. Sometimes there is. Flawed reasoning is everywhere because proper reasoning isn't as easy as it seems. Sometimes sound reasoning results in a startling conclusion that defies intuition or conventional wisdom.

When your stance is different than a consensus of experts, maybe you ought to take another look at your stance. We'd all be better off if we were more open to the possibility that we're wrong.