power series - How can we know the answer to 1-1+1-1+1 ...
$\begingroup$ The series does not converge, because as you observe, the partial sums $1,0,1,0,\ldots$ oscillate and do not approach a single limit. There are various ways to assign values to some divergent series, such as Cesaro summation, regularization, etc.
I have proved that 1 + 1 = 0 [closed] - Mathematics Stack Exchange
On the other hand, if 0+0=1, then we would have 0=1, which is prohibited by the field axioms. On the other other hand, there are algebraic structures - non-unital rings (rngs) - in which 0=1 is possible; on the other other other hand, that only happens for the trivial rng, so …
abstract algebra - Prove that 1+1=2 - Mathematics Stack Exchange
2013年1月15日 · The main reason that it takes so long to get to $1+1=2$ is that Principia Mathematica starts from almost nothing, and works its way up in very tiny, incremental steps. The work of G. Peano shows that it's not hard to produce a useful set of axioms that can prove 1+1=2 much more easily than Whitehead and Russell do.
real analysis - Function for the sequence (0,1,0,1,1,0,1,1,1,0 ...
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Formula for sequence $0, 0, 0, 0, 1, 0, 0, 0, 0, 1,\ldots ...
2015年9月5日 · There is a sequence with the values $0, 0, 0, 0, 1, 0, 0, 0, 0, 1, \ldots$ (basically there are always four 0s followed by a 1, then it repeats). Is there a function for this sequence? Here are two experiments for similar sequences:
What is formula for repeating sequence $0, 0, 1, 1, 0, 0, 1, 1 ...
2021年3月4日 · can somebody help me with this? I was searching through the web and I did not find anything useful. What is the formula for the sequence: $0, 0, 1, 1, 0, 0, 1, 1, ...$ or $0, 0, 0, 0, 1, 1, 1, 1, 0...
Formal proof for $(-1) \\times (-1) = 1$ - Mathematics Stack …
$\begingroup$ By defining a negative integer as an equivalence class like so you allow them to exist in some rigorous sense, and then by selecting an element of the equivalence class of -1 you extend FOIL to prove.
pattern recognition - Getting the sequence $\{1, 0, -1, 0, 1, 0, -1, 0 ...
The logic behind it is: n mod 2 gives 0, 1, 0, 1.. because we want all odd numbers to be 0 we use n+1 mod 2. Than we use (1 - (n mod 4)) to make 0 input to output 1 and 2 input to output -1. n mod 4 is just to limit the numbers between 0 and 3. Cheers.
I have learned that 1/0 is infinity, why isn't it minus infinity?
Sometimes in calculus $\frac{1}{0}$ is $+\infty$, sometimes it is $-\infty$ and sometimes it doesn't exists. But while the meaning is somehow closed to the idea of $\frac{1}{0}$, in calculus $\frac{1}{0}$ means something else that division. After reading few post on this we came to know that it depends on the context of its use.
General formula for nth element of the sequence 0, 1, 0, 1,
2018年9月25日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.