# Thread: 1 = 2

1. Originally Posted by Jonny
@Alea_iacta_est regarding 1=2

When you divide by zero, anything is possible.
Hence me saying, "Highly Amusing"

Technically, if one were to divide 1 by 0, the result would be infinite, for 0 can go into 1 an infinite amount of times (because infinite never ends, it would actually work). However, it is a paradoxical infinite because you cannot divide 1 by infinite to get 0. I saw this a long time ago, and I found the same discrepancies. I just wanted to share it with you guys to spark some mathematical debate.

2. Originally Posted by Alea_iacta_est
Hence me saying, "Highly Amusing"

Technically, if one were to divide 1 by 0, the result would be infinite, for 0 can go into 1 an infinite amount of times (because infinite never ends, it would actually work). However, it is a paradoxical infinite because you cannot divide 1 by infinite to get 0. I saw this a long time ago, and I found the same discrepancies. I just wanted to share it with you guys to spark some mathematical debate.
In this case, you're multiplying both sides by zero, THEN dividing by zero, so you're not dividing one by zero, but zero by zero.

0*x = 0*y for all x and all y.

3. Originally Posted by Alea_iacta_est
Hence me saying, "Highly Amusing"

Technically, if one were to divide 1 by 0, the result would be infinite, for 0 can go into 1 an infinite amount of times (because infinite never ends, it would actually work). However, it is a paradoxical infinite because you cannot divide 1 by infinite to get 0. I saw this a long time ago, and I found the same discrepancies. I just wanted to share it with you guys to spark some mathematical debate.
In this case, you're multiplying both sides by zero, THEN dividing by zero, so you're not dividing one by zero, but zero by zero.

0*x = 0*y for all x and all y.

4. Originally Posted by Alea_iacta_est
Hence me saying, "Highly Amusing"

Technically, if one were to divide 1 by 0, the result would be infinite, for 0 can go into 1 an infinite amount of times (because infinite never ends, it would actually work). However, it is a paradoxical infinite because you cannot divide 1 by infinite to get 0. I saw this a long time ago, and I found the same discrepancies. I just wanted to share it with you guys to spark some mathematical debate.
Technically, if one were to divide 0 by 0, as is shown in step 5 of the first post, you wouldn't get infinite. It would simply be undefined.

5. My high school math teacher used to tell us things like:

1 + 1 = 1
Add 1 pile of sand to 1 pile of sand. The result: 1 pile of sand.

2 1/2 != 5/2
If you have 2 1/2 cats, the 1/2 is obviously dead, but the 2 might be alive and need food, water, vet visits, playtime, etc. If you have five half cats, by contrast, they are all dead.

6. @Jonny
That was indeed the point. We pick one version and stay consistent, or we will have trouble.

That's why I added some generalizations of the misleading "proofs". Here, instead of two choices, we'd have n.

I believe the "error" is the swapping order of taking something to the n-th power and the n-th root. This is not something that can generally be done. sqrt(x^2)=/=sqrt(x)^2 unless x is positive.

7. This one is kinda silly and easy to spot the error, but it makes for a good joke...

A logic professor teaches a Tuesday Thursday class, and says at the end of class on Thursday he'll give an a "surprise" in class exam the following week. (He's a bastard).

Reasoning that if the exam will be given on Thursday, they would be able to deduce it on Tuesday, and it won't be a surprise, the students rule out that day.

But, again, they know it's on Tuesday now, so that won't be a surprise. The students conclude that this was just a way the professor was getting them to use their powers of deduction, and that there really won't be a surprise exam.

The students were then surprised by the exam when it occurred.

8. Originally Posted by ygolo
Reasoning that if the exam will be given on Thursday, they would be able to deduce it on Tuesday, and it won't be a surprise, the students rule out that day.

But, again, they know it's on Tuesday now, so that won't be a surprise. The students conclude that this was just a way the professor was getting them to use their powers of deduction, and that there really won't be a surprise exam.
Conclusion: the students should probably just drop the course before it wrecks their GPA. They may also consider switching majors.

9. ## 1 + 2 + 3 + 4 + 5 + 6 + ... = -1/12

Saw a video today which reminded me of this little gem:

The issues that underlie the problems with this proof are complex, shall we say. I don't want to string you guys along, but since some of you are rather analytic, continuation of this sort of cryptic verbiage will likely be welcomed.

10. Originally Posted by Jonny
The issues that underlie the problems with this proof are complex, shall we say. I don't want to string you guys along, but since some of you are rather analytic, continuation of this sort of cryptic verbiage will likely be welcomed.
LOL. Do you think we would ever converge on an understanding, or is there something absolutely incoherent in this "proof"?

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