Proofing on the Side

While completing exercise 3 earlier this week, I ran into some stylistic proofing problems. Some parts to a proof are straightforward to follow while others need a little more explanation to be logical / believable. The following is an sample of a proof taken directly from my answers in exercise 3:

Note: srt = square root

Step 1: 2n + 3 # Def of f(n)

Step 2: = 2srt(n)srt(n) + 3 #Algebraic Equivalence

Step 3: > 2srt(n)srt(n) #Subtract 3
Step 4: > 10csrt(n) # Refer to (***) below

As you can see, Steps 1 through 3 are very simple to understand. Step 4 however appears to be quite a stretch. This is where my stylistic problem occurred. I was able to prove this statement, but not in the same method as the previous steps. Now whenever I have this problem, I will do the following: Refer to look at the proof somewhere else on the page, indicated by my "Refer to (***) below" reference. Next, label this proof (***) and go about proving it. Sounds simple no?

So now at the bottom of that question I have the following:

(***): n > 25c^2 # n = (ceiling of 25c^2 + B + 1) > 25c^2

iff n > (5c)^2 # Algebraic Equivalence

iff srt(n) > 5c # Srt both sides

iff srt(n)srt(n) > 5c(srt(n) # Multiply both sides by srt(n)

iff 2srt(n)srt(n) > 10csrt(n) #Multiply both sides by 2

Thus Step 4 above is proven!

With this side proof, as well as the proof above, the statement for the assignment was proven and everything was legible for the marker. I like this "proof on the side" method. It's very useful and easy to understand. I'll be sure to use it in future assignments, and I encourage all who may be reading this to do the same. Good luck to all. 'Night :)