Why does "split" leave a gap?

Hi, I’m new at Audacity. I’m using it to edit my own recordings. Whenever I use the Split function (ctrl + I), it doesn’t just make a split, but leaves a big gap. Well, actually, not every time, and I can’t figure out what conditions cause it to leave a gap, sometimes it does, sometimes it doesn’t. I don’t want it to take any automatic control of how much comes out, just to make a split, and of course, I will be the one to decide how much I’m cutting out. What I do is zoom in and set the cursor at the place I want to split. I don’t highlight a section or anything; it’s just the cursor on the spot I want to split. But when I press “ctrl+I” or split from the edit menu, it leaves this gap (but strangely, only sometimes). What’s the gap for? Should I not worry about it, since the gap is not even .001ms? But why any gap at all? I want the places where I cut and joined to sound seamless, to have control over what comes out, obviously.
Also, suppose I’ve made two split lines and then cut out the section in between because I want what was on the right side of the right split line to move to the left and join up with what was on the left side of the left split line. Well, when I’ve cut the section out, I zoom in and see that it hasn’t moved what was on the right side of the right split line all the way over to what was on the left side of the left split line, but has also left a tiny gap there. When I click on either split line (on the left or right side of the gap), it joins the two waveforms, but I’m not sure if it’s joined them by moving the right waveform over a little more left until it joins to the left waveform, or if it’s doing something else, like extending the left waveform.
Finally, suppose I want to cut out a section of a song, while leaving the rest (everything to the left and right of the cut section) in place. Then I want to replace the cut section with a piece that turns out to be slightly longer than the cut section. How do I move everything to the right of it over out of the way (especially if everything to the right is all pieces that have cuts and are together temporarily, but not “joined” and so they don’t move as one), and then when I paste the new section, bring what is to the right of it over to join?
Sorry if these questions are answered somewhere and I didn’t see, or if this is pretty basic stuff. I’ve been reading the “Navigation Tips” and am not finding the answers.

***NEW PROBLEM (started after posting this question on the forum): Now when I set the cursor at a spot and hit “ctrl I” it doesn’t even make the split (well, gap) at the place where the cursor is, but away to the left in a totally different place! What?! How do you use this?

****Sorry, but there’s one more thing that is just really confusing the hell out of me: At the Navigation Tips wiki, it says:
“Split lines disappear when you click on them to merge clips together, but you can use current Audacity’s Cut Lines feature to place a vertical line at which audio was cut out. Click on the line at any time to restore the cut audio. Cut Lines are enabled on the Tracks tab of Preferences.”

Well, I followed these instructions and enabled Cut Lines so I can keep track of where I’ve cut out audio, but I’m seeing no vertical lines at places where audio was cut out and merged. I’m confused, isn’t the “Enable Cut Lines” feature so that I can see where there was a cut, even after merging? If not, what’s it there for?

The “gap” should be just one sample period, that is, if you zoom in close enough to see the individual dots (representing the samples) then a split should simply break the line that joins the dots but none of the dots removed. Joining the split back together (for example with Ctrl+J) restores the line that joins the dots.
The “line” does not really exist, it is just there as an illustration of a continuous waveform, but really digital audio is just “dots”, that is, a series of numerical values at points in time.

Thanks, ok, but it doesn’t break the line where I had the cursor. If I have the cursor between two dots and hit “split”, it makes the split between the two dots to the left of the two dots the cursor is between.

I was thinking this has something to do with an automated “find zero crossings” function, but the place I’m trying to have it split is at zero, so why won’t it split the section between the two dots where I have the cursor? I’m trying different places now, some at zero, some not, and sometimes it splits between the two dots where I placed the cursor, and other times it splits between the two dots to the left of the two dots I have the cursor between–independent of zero.

This is tricky and it took the developers a lot of time and effort to get this to work exactly right in all situations.
The difficulty is that we are dealing with samples that are literally “points” along the time line, they have zero duration, but at the same time we are dealing with a “continuous sound” in which you can select any point along that time line. It also has to work with splitting, cutting, deleting and pasting, possibly with multiple tracks with different sample rates. The way this is handled is that Audacity looks for the nearest sample (the dot) and then disconnects that dot from the previous dot.

If you are zoomed in close enough to see the dots, imagine the mid-point between two dots, If you click to the left of that mid-point then the sample to the left is selected for splitting. If you click to the right of the mid-point then the dot on the right is selected for splitting. The “split” action then “disconnects” the selected dot from the previous dot on the timeline. This may seem a bit strange, but importantly the same scheme works whether splitting, cutting, copying, pasting, deleting on one or more tracks, whether of the same sample rate or different.

Thank you, Steve. Yes, right after that last post, I figured out that if you click right or left of the mid-point, it will determine which sample is cut. Thanks.