Show every subsequence of a subsequence of a given sequence is itselfa subsequence of the given sequence. Hint: Define subsequences asin (3) of Definition 11.1 g

Suppose that ,   and are all sequences, also suppose that   ⊂ ⊂  ∀ ∈ . This implies that ⊂ as required. 

Step-by-step explanation:

If you suppose that ,   and  are all representing three sequences respectively, and you also suppose that   is a subset (in other words subsequence) of and  is a subset (in other words subsequence) of , where n takes its values from the set of positive integers. We can safely say that is a subsequence of and this can demosnstrated mathematically as follows:

Suppose that ,   and are all sequences, also suppose that   ⊂ ⊂  ∀ ∈ . This implies that ⊂ as required. 

the figures below are made out of circles, semicircles, quarter … find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations). remember that we'll also have to cut whatever areas we get in half, since we're only dealing im pretty sure that is the right answer

step-by-step explanation:

konichiwa~! my name is zalgo and i am here to answer your anime-related question today. more than likely, kirishima would kill izuku, marry mino and kiss momo. all of this would be my opinion by the way. (and i am also a weeb lol)

i hope this you! : d

stay and stay proud! " - zalgo

(and do you think you can mark me as brainliest? i'd greatly appreciate it! arigato~! )