Alex wrote the following indirect proof:
Prove: 13 is a factor of 195
Step 1: Assume that 13 is not a factor of 195.
Step 2: 195 divided by 13 is 15.
Step 3: A factor is an integer by which another integer is a multiple.
Step 4: Therefore, 13 must be a factor of 195.
Which step in Alex's proof is incorrect?

Question

Alex wrote the following indirect proof:
Prove: 13 is a factor of 195
Step 1: Assume that 13 is not a factor of 195.
Step 2: 195 divided by 13 is 15.
Step 3: A factor is an integer by which another integer is a multiple.
Step 4: Therefore, 13 must be a factor of 195.
Which step in Alex's proof is incorrect?

anonymous · Answer

You always start out with proving the negation of what you want to prove. So you want to assume the negation of "13 is a factor of 195."

tkhunny · Answer

Step 3 isn't a step.  The Alex is just trying to impress us with how much he knows.

If 13 is NOT a factor of 195, it CANNOT be expressed as an integer multiple of 13.

13*n = 195 does NOT exist for n an integer.

195 = 13*n + m, for n an integer and m in {1,2,3,4,5,6,7,8,9,10,11,12}

Well, if it's one of those, which one is it?  What?  We discarded ALL of them?  We found NONE?!  I am shocked!!!!

Well, then, since our premise requires foolishness, I guess we should reject our premise.