KAMP

Kategori Umum => Matematika => Topik dimulai oleh: trfrm pada Juli 19, 2018, 06:26:48 PM

Judul: DIVISION BY 0
Ditulis oleh: trfrm pada Juli 19, 2018, 06:26:48 PM

In real algebra, the null (0) can be reached from left and from right ... .

In complex algebra, the null (0) can be reached from all directions ... .

Judul: Re:DIVISION BY 0
Ditulis oleh: trfrm pada Juli 19, 2018, 06:28:53 PM

$(1 - 1 + 1 - 1 + \cdots)$ is not 0 ... because we don't know when the series ends ... . :)

Judul: Re:DIVISION BY 0
Ditulis oleh: trfrm pada Juli 19, 2018, 06:36:28 PM

Kutip dari: river_rat

But one infinite series I do find confusing is $1 - 2 + 3 - 4 + 5 - \cdots$, which apparently sums to $1/4$ !

\[ 1 - 2 + 3 - 4 + 5 - 6 + \cdots \]
\[ = (1 + 3 + 5 + \cdots) - (2 + 4 + 6 + \cdots) \]
\[ = \sum_{j=0}^\infty (2j - 1) - \sum_{j=1}^\infty 2j \]
\[ = -\sum_{j=1}^\infty 1 \]

is negative infinity ... ,

so this series is divergent ... .



I'm sorry if I do mistake ... .  :(