Today's Puzzle

tom982 said:

Arc said:

Lol, that's a fallacy

From the equation, we are subject to determine the values of the variables, x and y. Isn't it? Not the values of the constants.

Taking your calculations, we get
Let x=y
Multiply both sides by x:
x^2=xy
Subtract y^2 from both sides:
x^2-y^2=xy-y^2
Factorise both sides:
(x+y)(x-y)=y(x-y)
Divide both sides by (x-y):
x+y=y
or, x=y-y
or, x=0
putting the value of x in the initial condition, we get
y=0

To determine any other values of x and y, we need at least one more equation.

I'm not asking you to solve simultaneous equations, or find solutions, I'm simply asking you to tell me where the maths is flawed for that proof that 2=1 :)

At the outset, we are told that x=y. Later on, there is a division by (x-y). Since x-y is zero, you are dividing by zero. This does not give any defined answer. That is where the maths is flawed.

clunkfish said:

Britton30 said:

Whatever. I didn't use an excalamtio point. it's a "|"

2|3 could be used to mean 2 is a divisor of 3 - which it isn't - but is basically meaningless. I assumed it was a typo. It is never used to mean 2 raised to the power 3.

Never is a strong word. Everyone has their own ways of writing things, be it individually or nationally, so who knows what it is meant to symbolise? Just because you and I know it as the symbol for divisors, it doesn't make it correct. I have absolutely no idea how they symbolise indices in the US - I would have guessed it was the same as we use here in the UK but from what Gary said, it seems like we're wrong.

Mathematical notation is not a free for all where everyone can just choose their favourite way of writing things, because that would clearly lead to chaos. 2|3 has a specific meaning - that 2 is a divisor of 3, which is obviously incorrect. It is not used to symbolise 2 to the power of 3 anywhere.

There's a wider point here. Don't promulgate ignorance. Challenge what is wrong, so that it doesn't get repeated. Don't defend what is wrong on the grounds that "who knows, maybe it's correct somewhere".

A Guy said:

There are nicer ways of saying things as well. It's not necessary to call someone ignorant, even if your information is correct. A Guy

Yes, and don't accuse me of things I haven't said.

Being ignorant of some particular thing is not the same as being an ignorant person. I merely pointed out that what was being said was in ignorance of the truth in this matter. I am ignorant of many many things, but am not an ignorant person. That's an important distinction.

Arc said:

tom982 said:

I'm not asking you to solve simultaneous equations, or find solutions, I'm simply asking you to tell me where the maths is flawed for that proof that 2=1 :)

That is simply a fallacy..... nothing else. Apparently it looks to be logical, but at the lower part of the solution it is not following the rules of mathematics.

Omitting variables from the both sides of an equation is not what mathematics do; but logic (theoretical logic) may do it rightly. As it is logically correct, but not as per mathemetical procedure, it is nothing but a fallacy.

Faced a few of such fallacies (including this particular one) during the initial days of UG studies. Forgot them all, now you made me recall this one :)

Let's keep this straight. The whole thing is wrong both mathematically and logically, because it involves a step where you divide both sides of an equation by zero. There is no "omitting variables" involved. Dividing anything by zero gives an undefined answer - it is simply meaningless. For instance:

2 x 0 = 3 x 0
Divide both sides by 0
2 = 3

Pure nonsense.

A Guy said:

clunkfish said:

A Guy said:

There are nicer ways of saying things as well. It's not necessary to call someone ignorant, even if your information is correct. A Guy

Yes, and don't accuse me of things I haven't said.

Being ignorant of some particular thing is not the same as being an ignorant person. I merely pointed out that what was being said was in ignorance of the truth in this matter. I am ignorant of many many things, but am not an ignorant person. That's an important distinction.

Justify it any way you want, it's still the tone you used. To mention someones ignorance, then say it doesn't make them ignorant is semantics. My original point remains. A Guy

No - your original error remains. I don't much like being accused of stuff simply because you don't appreciate the subtleties of the language I used, dismissing it as "semantics". Semantics is meaning: here the semantics are important. Like I said, one can be ignorant of something without being an ignorant person.

Besides, what I actually said was that the wider point was "don't promulgate ignorance". I described it as a "wider point" precisely in order to depersonalise it.