Dear Corvus, your queries are quite interesting. However, within the scope of a single article, it was not possible to address all the points. They require separate articles for a thorough discussion.

The comparison of a dream with a removable discontinuity is an analogy, not a complete identity.

I don't.........................................a continuity
The title of my article is An Analogy with Removable Discontinuity, so it is of no use to argue that the so-called continuity of the waking state is broken by sleep. The basic concept of removable discontinuity, as discussed in mathematics, should be taken into account; otherwise, our understanding may go haywire. Separate instances are akin to mathematical points forming a continuous function. A continuous function can be increasing in some intervals and decreasing in others, whereas the function of the waking state is bound to be increasing. Thus, it is smoother than some other continuous functions. Here, memory plays the role of a weaving thread that keeps the different instances together.

I believe................................... waking experience.
In response to this objection, the opening lines of my article should be read: "Like dreaming, awakening is also a feeling, yet it is perceived as real." I have attempted to explain why the feeling of the waking state appears to be different from its dreaming counterpart.

Thanks for your thoughtful and encouraging words.