If a divides b and b divides c then a divides c

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Sorry for the video coming out late, I was studying for exams!!

This video will cover the question if a divides b and b divides c then a divides c. This is a proof we can think is trivially true but that does not count in math! Lets get to it. If you liked to see any other questions covered please comment below.

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Would this work?

Let {a, b, c, k, l, m} all be integers.

GIVENS: a|b ak = b k = b/a

GIVENS: b|c bl = c l = c/b

PROVE: a|c am=c m = c/a

To prove that a|c, we would have to show that m is an integer.

We have to show that (c/a) simplifies to be an integer.

c/a

bl / (b/k)

Copy Dot Flip

bl * (k/b)

l*k

Integers Closed Under Multiplication

We find that m was an integer.

Thus, it is true that a|c.

Is this a legitimate way to write the proof?

Thank you so much!!

keldonchase

thanks very much(you have really helped me understand some concepts in discrete tyln, daystar universiy kenya

kekstartyln

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