Except 2S - 1 also = S. Fun, isn't it?Now, since 2S + 1 = S, it follows that S = -1
In other words, 1 + 2 + 4 + 8 + ... = -1
Of course, that result isn't quite as astonishing as 1 + 2 + 4 + ... = -1It is the same as:
0.99999.... = 1
Basically, you cannot assert that 2S + 1 = S, since S is a different sum than 2S + 1. For example, if we admit that S is a finite sum of 4 members, 2S + 1 would equal to a sum of 5 members and not equal to S.Let S = 1 + 2 + 4 + 8 + ...
Then 2S = 2 + 4 + 8 + 16 + ...
And 2S + 1 = 1 + 2 + 4 + 8 + ... = S
Now, since 2S + 1 = S, it follows that S = -1
In other words, 1 + 2 + 4 + 8 + ... = -1
In fact, it is entirely reasonable and legitimate to assert that 2S + 1 and S are equal. They have exactly the same cardinality.Basically, you cannot assert that 2S + 1 = S, since S is a different sum than 2S + 1.
I don't admit this at all. S is not a finite sum, and this is alluded to by the ellipsis (...), meaning "continuing in the same pattern."For example, if we admit that S is a finite sum of 4 members, 2S + 1 would equal to a sum of 5 members and not equal to S.
I'll admit that S(n) = 1 + 2 + 4 + 8 + ... + 2^n + ...Lets admit that:
S(n) = 1 + 2 + 4 + 8 + ... + 2^n
You're omitting lots and lots of terms here.Therefore:
2S(n) + 1 = 2 x (1 + 2 + 4 + 8 + ... + 2^n) + 1 = 1 + 2 + 4 + 8 + 16 + ... + 2 x 2^n
Mark, are you not astounded that two completely different numbers are in fact the same?!Of course, that result isn't quite as astonishing as 1 + 2 + 4 + ... = -1
Always!Mark, are you not astounded that two completely different numbers are in fact the same?!
Dave
I think your calculator's circuitry has been contaminated. Perhaps by hairdressers...Of course, don't forget that 6 x 9 = 42
Is this the same as "There are only 10 types of people in the world: Those who understand binary, and those who don't"Everyone knows that 1 + 1 = 10
by Jake Hertz
by Aaron Carman
by Aaron Carman