Something out of nothing

[janesmythe22]

I'm quite sure that myriad other definitions exist, but it feels that they all make something out of nothing:
Point: a place in space with zero dimensions, shape, size, or extension (0D)
Line: an infinite path connecting an infinite number of points (1D)
Plane: (mathematics) an unbounded two-dimensional shape (2D)
Cube: a three-dimensional figure that has squares for all of its faces (3D)
Zero times no matter what should equal zero? (Unless defined otherwise). So, was it defined otherwise somewhere? Like 0! =1.

[bernardo]

Yes: Zero times anything is zero.  What has all that other stuff got to do with your question?

[MargeB]

It's implied. What she means is that any 1D,2D,3D 'object' has as its principle the point (0D). It has 0D. So how come the others have non zero values?

Mystery of the universe tied up in there somewhere.

That's my take on it anyway.

[jake-the-peg]

I feel the flaw in this argument is the use of the multiplier.

I don't quite understand why you've used that.

[Space]

zero times any finite number is zero.
But you don't multiply by finite numbers in your example about points...

[Dacetine]

A point may be regarded as zero-dimensional but this means only that it is infinitesimally small, not that it does not exist (as "zero" implies in the question).

So, an infinite number of infinitesimal points can be joined up to produce a line. I think this is pretty mind-bending but not illogical.

[fo3nix]

0 x anything = 0

this is true for algebra, in mathematics.

what you are talking about here are dimensions. it's not the same thing.

[c00ky83]

When doing a maths question with logarithms I accidentally proved that 0=1.  I won't go into it but there was definitely no flaw in my working and it blew my mind!

[fo3nix]

c00ky83: there definitely would have been a flaw in your maths. maybe not the actual algebra itself, but in the use of the algebra emplyed (and thus your understanding of its use).

[c00ky83]

OK - here goes.  ln(1)=0.  1=(-1)^2, so ln(1)=ln[(-1)^2], but this is 2ln(-1).  So ln(-1)=ln(1)=0 - follow that?  So what I meant earlier was -1=1, not 0=1, I forgot.  I know it's rubbish, but like I say it blew my mind!

[fo3nix]

ln(1)=0
1=(-1)^2
ln(1)=ln[(-1)^2] = 2ln(-1)

ln(-1)=ln(1)=0

---------------------------------

I think the problem is in the 3rd line there. You should perform the power calculation first, thus ln(1)=ln(1)=0.

[Brugel]

ln (-1) is undefined. log (x) only exists provided x is greater than 0.

The rule log (x^n) = nlog (x) is also only valid provided x is greater than 0.

[janesmythe22]

Thanks MargeB. You've got it right-as always (what I meant). It feels that this 'reality' foundation is a wee bit wobbly. 

[MargeB]

Sure is! This all reminds me of Zenos Paradox.

[bernardo]

x = y

x^2 = xy

x^2 - y^2 = xy - y^2

(x + y)(x - y) = y(x - y)

(x + y) = y

2x + y = x + y

2x = x

2 = 1

[newtron]

bernardo, if the fourth step, you cannot divide both sides by (x-y) because x-y=0 and the result of anything divided by zero is undefined.

[janesmythe22]

Yes MargeB, I do remember the Zeno 'paradox' from my early school days. Like I said in my question, the fact is that mathematics 'fits' to our reality only if it gives its 'definition' of entities. In that case, to repeat myself, it all works well 'by definition'. If my memory serves me well (this has nothing with 'This Wheel's On Fire'), that was the reason why Kant regarded mathematics to be only true 'science'.

So, let's see-do athletes are 'really' getting faster etc., or our measurement gadgets are just being capable to add more digits after the decimal point.

[janesmythe22]

Oh, dear-I'll get my grammar textbook straightaway.

[bernardo]

bernardo, if the fourth step, you cannot divide both sides by (x-y) because x-y=0 and the result of anything divided by zero is undefined.

Precisely my point.

[MargeB]

did ur point have any dimensions?