How many jogs make a jogger?

I've been wanting to get into jogging for a while now. I work ten hours (sometimes more) a day on weekdays, and at least four hours every Saturday and Sunday. I have a toddler, a partner, and a house that does not clean itself. (R tries, but it's a lot for one man to handle while simultaneously watching a 2-year-old.) I also am trying to get back into cooking actual food at least one meal a day. And I need to sleep sometime. So my free time is, suffice to say, limited.

Which is where jogging comes in. I can, and do, walk for fitness, but even at the (fairly fast) pace I set, it takes a while. Jogging can net me more distance in less time. It also provides a greater bang for my buck, exertion-wise. So I'm definitely interested.

I'm also recovering from injury (sprained ankle), have a bad knee (for which I've done physical therapy in the past, and therefore don't want to anger again), and have endometriosis -- sometimes walking is the best I can do. I get that. But I am trying to work in more jogging. On my good days. Just to start building my stamina.

I've now jogged three times. Roughly half a mile each time -- nothing big. (I also walk a mile or three on these outings; I don't just do a couple laps and call it a day.) Does that make me a jogger now? Or do I need to jog a few more times? If so, how many? Will it ever stop feeling weird to use the word "jogger" in association with myself?

Perhaps this will influence my jog cred: The other day, I slipped out while my child and her father napped to squeeze in a jog. Today, I got up at 4 a.m. to do so.

I'm not sure what I think about that.

But working out at 4 a.m. makes sense in the same way jogging makes sense: It saves time. If I save my workout for the evening, I have to contend with my child, who has been without me all day and is ready for some Mumma time. Even if I can get her to play at the playground while I work out, she usually wears out before I do. If I do it before she wakes up, she never knows I'm gone. And I can still start freelancing at 5 a.m. as usual.

So I do understand the early-early-morning joggers. I'm sure their circumstances aren't much different than mine. I'm just not really sure how I went from computer chair potato to someone who goes jogging in the middle of the night.