Split exact sequence
Imagine you have a long rope with three knots tied at different points along it. Each knot creates a section of the rope with a start and an end. This rope represents what we call a "sequence".
Now, imagine you have a special knife that can cut the rope exactly at each knot, separating the rope into three pieces.
If you take all three pieces and put them back together in the correct order, you will end up with the same rope you had at the beginning.
This is similar to what we call a "split exact sequence" in math. We break down a sequence into smaller pieces, but the pieces still fit together perfectly to give us the full sequence back. It's like taking apart a puzzle and putting it back together again with all the pieces in the right place.
This is an important concept in math because it helps us understand how different parts of a sequence are related to each other, and how we can manipulate and analyze them more easily.
Now, imagine you have a special knife that can cut the rope exactly at each knot, separating the rope into three pieces.
If you take all three pieces and put them back together in the correct order, you will end up with the same rope you had at the beginning.
This is similar to what we call a "split exact sequence" in math. We break down a sequence into smaller pieces, but the pieces still fit together perfectly to give us the full sequence back. It's like taking apart a puzzle and putting it back together again with all the pieces in the right place.
This is an important concept in math because it helps us understand how different parts of a sequence are related to each other, and how we can manipulate and analyze them more easily.