I was doing some random math today and found a flaw in the mathematical concept of FOIL. I was curious if anybody knows of any more.

FOIL:

http://pastebin.com/BhGeFTDm
Are there any more people can add?

**technomonkey76 wrote:**

**Code:** ```
a = b # Okay, so a equals b…
```

a^2 = ab # Makes sense…

...

(a+b)(a-b) = b(a-b) # Wait…

In this line, a-b = a-b = 0, so you get 0 = 0. No flaw.
**KermMartian wrote:**

**technomonkey76 wrote:**

**Code:** ```
a = b # Okay, so a equals b…
```

a^2 = ab # Makes sense…

...

(a+b)(a-b) = b(a-b) # Wait…

In this line, a-b = a-b = 0, so you get 0 = 0. No flaw.

True. Oh well. I tried too hard to see something wrong.
It took me a while to figure it out.

Those kinds of things are often errors in stuff like a^2=4 -> a = 2 (where of course a = +/- 2).

Not to mention, you try to divide by 0 when you simplify that last line (# Wait...) to

**Code:** `(a+b) = b`

because you divide by a-b which is a-a which is 0.
Ah, and that's probably the larger flaw that keeps the simplification from being correct all the way through. Nice catch there, tanner!

Thanks

It took me a while to find it, but for these "flawed" math things, it usually is a divided by zero problem, so I just looked for that

Edit: Good job, of course, on your find. I wouldn't have thought it that far

**KermMartian wrote:**

Ah, and that's probably the larger flaw that keeps the simplification from being correct all the way through. Nice catch there, tanner!

Should I delete this topic, then?
No need. Just leave it to learn from.

**technomonkey76 wrote:**

I was doing some random math today and found a flaw in the mathematical concept of FOIL. I was curious if anybody knows of any more.

FOIL:

http://pastebin.com/BhGeFTDm
Are there any more people can add?

You started with a=b and you later divided out (a-b) which is zero. That is NOT a flaw in foil. It is a math error on your part. Division by zero is not a mathematically defined operation.
Dingus, yes, I think we established that already.

I think it would be interesting to go through some of the other commonly-cited examples of supposedly flawed math so we can find where the errors are.

**Dingus wrote:**

Division by zero is not a mathematically defined operation.

*Division by zero is not defined in real number arithmetic.
Yeah, I love little errors like that. It's like the .999 repeating == 1 thing.

.9 repeating is equal to 1, that's not an error.

**merthsoft wrote:**

.9 repeating is equal to 1, that's not an error.

^ Exactly this. In third grade or so (?) I actually debated with the teacher for about ten minutes about this before I was finally convinced. Here's another fallacies proof:

**Code:** ```
Step 1: -1/1 = 1/-1
```

Step 2: Taking the square root of both sides: sqrt(-1/1) = sqrt(1/-1)

Step 3: Simplifying: sqrt(-1) / sqrt(1) = sqrt(1) / sqrt(-1)

Step 4: In other words, i/1 = 1/i.

Step 5: Therefore, i / 2 = 1 / (2i),

Step 6: i/2 + 3/(2i) = 1/(2i) + 3/(2i),

Step 7: i (i/2 + 3/(2i) ) = i ( 1/(2i) + 3/(2i) ),

Step 8: (i^2)/2 + (3i)/2i = i/(2i) + (3i)/(2i),

Step 9: (-1)/2 + 3/2 = 1/2 + 3/2,

Step 10: and this shows that 1=2.

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