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Jerl commented at 2013-08-08 16:55:44 » #1376326
The answer can be yes or no depending on what timeline you're in.
Yes and no can also be represented by 1 and 0, respectively.
Another function with this property is Grandi's series, an infinite sum such that s = 1 - 1 + 1 - 1 + 1 - 1...
An interesting thing about this infinite sum is that, depending on where you place the brackets, you can get an answer of either 1 or 0.
For example, if you place the brackets such that the function reads s = (1 - 1) + (1 - 1)..., the answer to the infinite sum is 0.
On the other hand, if you place the brackets such that the function reads s = 1 + (1 - 1) + (1 - 1) + (1 - 1)..., you get an answer of 1.
But both of these answers are pretty arbitrary. There is actually a third answer. And it probably isn't an answer that you will expect.
Let's take 1 - s. This would be 1 - (1 - 1 + 1 - 1 + 1 - 1...).
Distribute the plus signs, and you get 1 - s = 1 - 1 + 1 - 1 + 1 - 1...
...which is the same thing as s. So, 1 - s = s.
Okay, let's add s to both sides so that we can calculate this properly.
1 = 2s.
And we can find the value of s to be 1/2.
So, the answer to your question is that there isn't an answer unless there is more context to base it on.
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The answer can be yes or no depending on what timeline you're in.
Yes and no can also be represented by 1 and 0, respectively.
Another function with this property is Grandi's series, an infinite sum such that s = 1 - 1 + 1 - 1 + 1 - 1...
An interesting thing about this infinite sum is that, depending on where you place the brackets, you can get an answer of either 1 or 0.
For example, if you place the brackets such that the function reads s = (1 - 1) + (1 - 1)..., the answer to the infinite sum is 0.
On the other hand, if you place the brackets such that the function reads s = 1 + (1 - 1) + (1 - 1) + (1 - 1)..., you get an answer of 1.
But both of these answers are pretty arbitrary. There is actually a third answer. And it probably isn't an answer that you will expect.
Let's take 1 - s. This would be 1 - (1 - 1 + 1 - 1 + 1 - 1...).
Distribute the plus signs, and you get 1 - s = 1 - 1 + 1 - 1 + 1 - 1...
...which is the same thing as s. So, 1 - s = s.
Okay, let's add s to both sides so that we can calculate this properly.
1 = 2s.
And we can find the value of s to be 1/2.
So, the answer to your question is that there isn't an answer unless there is more context to base it on.
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