It looks like you're using an Ad Blocker.
Please white-list or disable AboveTopSecret.com in your ad-blocking tool.
Thank you.
Some features of ATS will be disabled while you continue to use an ad-blocker.
saneguy
So you have shown that programming is not mathematics.
ChaoticOrder
You can make it increment the number over and over again but it'll never give you the true answer to 1+2+3+4...∞.
Whether you think the answer is -1/12 or infinity, it wont give you either of those answers will it? It doesn't understand such abstract equations which continue for infinity, there is no way to encapsulate an infinite series into a simple set of calculations.
ChaoticOrder
Just because a computer is a calculator does not mean it's capable of doing all types of mathematical calculations.
ChaoticOrder
You can make it increment the number over and over again but it'll never give you the true answer to 1+2+3+4...∞.
ChaoticOrder
In fact it can't even tell you the correct result for 4/3, it'll just give you a floating point number which is an approximation of the real answer, ignoring the fact that the 3 repeats for infinity.
WeAre0ne
ChaoticOrder
You can make it increment the number over and over again but it'll never give you the true answer to 1+2+3+4...∞.
In a manner of speaking, it will give you the true answer to 1+2+3+4...∞. You just have to leave the computer running for infinity. Which is forever.
Hmmm, I'm not sure I can wait that long for the answer. I'm not sure there is an answer, since it's an abstract concept. But yeah no matter how long you let the program run it's never going to end up with a negative number as long as it's summing positive numbers.
WeAre0ne
In a manner of speaking, it will give you the true answer to 1+2+3+4...∞. You just have to leave the computer running for infinity. Which is forever.
The graphs seem to be a good way to look a this, however, note that the Ramanujan sum and the zeta regularized sums appear on the graphs I posted on page 3 when n tends to zero, not when n tends to infinity. When n tends to infinity the graph tends to infinity, so you can visualize all three sums at the same time.
bastion
These are infinite series though - it's far quicker to calculate by hand and plot graphs based on when n tends to infinity. Hence to convergence from a divergent series.
It doesn't ignore the fact that 3 repeats for infinity. If you wanted it to, it will compute the result of 4/3 to infinite decimal places, but none of us have time for that.
saneguy
Personally, I find the result that 1-1+1-1.....=1/2 makes sense. It's like saying if you jump from 0 to 1 forever thats equivalent to 1/2. It's kind of a cool way to deal with infinity.
In colloquial language average usually refers to the sum of a list of numbers divided by the size of the list, in other words the arithmetic mean. However, the word "average" can be used to refer to the median, the mode, or some other central or typical value. In statistics, these are all known as measures of central tendency. Thus the concept of an average can be extended in various ways in mathematics, but in those contexts it is usually referred to as a mean (for example the mean of a function)
Miniscuzz
It was all basic Algebra even a 5th grader could understand.
saneguy
Personally, I find the result that 1-1+1-1.....=1/2 makes sense. It's like saying if you jump from 0 to 1 forever thats equivalent to 1/2. It's kind of a cool way to deal with infinity.
OptimusCrime
...This mathematical induction trick with moving numbers to the right is a joke...
The answer people are looking for in the real world is not based on an average, but on a real straightforward sum. The answer of "-1/12" is a function of the math itself, NOT a function of what really happens when I add whole things together.
saneguy
There are several people posting here who do not understand advanced mathematics. It is quite humorous to see people criticizing the work of some of the best mathematicians in history.