Everybody knows that it doesn’t make sense. By ‘trick’, did you think I meant I actually made 1 equal to 2?

Saying there is no trick is what people do when they know there is a problem in the logic but can’t identify where it is… so they just say: er, uh, ee… it’s just wrong!

You need to be like Carleas… point out exactly where in the proof (or “proof”) I made an invalid move.

Huh? I didn’t drop any b. I “dropped” (a - b) under each side of the equation to get a + b = b. Nowhere did I get b = b(a - b).

It would produce nonsensical results such as this:
(3+4)(3-4)=4(3-4)
-7=-4

The crux of what you are doing, is exposing a flaw in mathematics. You set the value of the equations to zero, so it erodes any qualities the equations originally had.
See my thread called “the number delusion”.

The same thing happens when you scale a 3 dimensional shape to zero. You can scale it to 10%, 50%, or even a negative, and still retain the shape. But once you set it to zero information is lost and the shape no longer exists. That is the crux of what you are doing here.

I don’t know why this wasn’t an open/shut thread. A nice little trick to figure out, for sure, but it doesn’t warrant in depth discussion unless you don’t understand it. It certainly doesn’t throw numbers into doubt.

This one might warrant discussion though.

It happens when you mess around with infinite series, notably “s = 1-2+3-4+5-6+7-…” and what happens when you add it to itself in a certain way (i.e. add the 1st term to the 2nd, the 2nd to the 3rd and so on) and noting that it results in “t = 1-1+1-1+1-1+1-…”, which you have to accept equals a 1/2, because it’s an average of whether you “stop” at the last even number in the series or the last odd number in the series.
Accepting these, you can say that 2s = t = 1/2, therefore s = 1/4.
Then you can subtract “s” from the infinite series in question of “u = 1+2+3+4+5+6+7+…”, the first term from the first term, the second from the second and so on - nothing special here. You get “u-s = 0+4+0+8+12+0+16+…”, so you can factor out the 4 and get “u-s = 4(1+2+3+4+5+6+7+…)”, which is “u-s=4u”.
This simplifies to “-s = 3u”, we know s = 1/4 so “-1/4 = 3u”, making our infinite series “u = -1/12”.

Obviously it rides on the problem of “t”. I don’t see why you can’t add “s” to itself in the way I described above… infinite series extend infinitely so it doesn’t matter what order you add each number together. The rest is just standard rearrangement and substitution.

I don’t think the infinite series “t” has a valid answer, which makes possible such things as “1+2+3+4+5+6+7+…” = -1/12. I’m pretty sure you can make it equal other different values too.

I don’t know about any flaw in mathematics… just a trick in a pseudo-proof.

Not sure what you mean by “set the value of the equations to zero.” There was a divide by zero, and if a = b, then some of the equations resolved to zero, but not all. Equations should be permitted to equal zero sometimes, but it’s the divide by zero which really screws things up.

I’m inclined to agree. Saying that 1 - 1 + 1 - 1 + 1… = 1/2 seems to make good folk sense, but I don’t think it follows from any arithmetic rule. The series 1 - 1 + 1 - 1 + 1… can be rewritten as (1 + 1 + 1 …) + (-1 - 1 - 1 - 1 …), which means infinity plus negative infinity which would give you zero (and maybe you can’t even say that). I think we have to assume that in order for the rules of arithmetic to hold, your expressions have to at least be complete. Saying 4 + 2 + 1 = 7, for example, says that when you have 4 of something, and you also have 2 of that something, and one more of that something, you have 7 of that something all together. But how are you supposed to say how much of something you have if you just never stop listing of how many in each group of somethings you have (well, you’d have infinity, but what happens when you include negatives)?

0 is the father of infinity, the ultimate mathematical pariah when it comes to application in physics.

For good reason though: as soon as you are dividing by 0, for example, your formula loses its predictive power. Magic indeed.

Funny though, that 0 is such a relief in basic addition and subtraction, although 1 is a God-send when it comes to higher level functions. A better magic trick.