Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: 0 The Empty Number; its purpose is to set bases
Replies: 46   Last Post: Sep 24, 2017 8:28 AM

 Messages: [ Previous | Next ]
 FromTheRafters Posts: 248 Registered: 12/20/15
Re: 0 The Empty Number; its purpose is to set bases
Posted: Sep 22, 2017 9:21 AM

After serious thinking conway wrote :
>> Zero is the name for no quantity. Its only real use
>> is to set bases.
>>
>> Mitchell Raemsch

>
>
> ANYTHING that is empty...still contains space. You can have "no quantities"
> of ANYTHING....that does not mean you have no quantities of space. There is
> always space.....you can NOT have NOTHING.....zero is a empty quantity of
> space....not an empty quantity of nothing.
>
> Zero's real use is as a "point of reference" on a number line.......to "set"
> bases.....here I agree....

I disagree. Zero's real role is additive identity. One's real role is
multiplicative identity.

Going out on a limb...

Two is the first number. There is no need to count one thing, but when
you have 'another thing' you have what we now call two and sort of
'back define' one as how many you used to have. Seemingly a
mathematician would also have the concept of ratio (I have two times as
many as before) and the concept of addition (I have one more than
before) follow naturally. The concepts of 'another another thing' and
another 'nuther 'nuther thing and so on follows and one can use as many
symbols as we want to represent the new inductively discovered (or
created) numbers.

With the concept of ratio (I have twice as many as before) and the
addition notion, the inverses are desired, so we create (or discover)
the integers for addition and subtraction and the rationals for
multiplication and division.

Enter the reals:

After seemingly filling the whole number line (or space) they discover
(or invent) the 'number' squareroot of two. It's not on the line
anywhere, there must be spaces (holes) in our number line. To fill
these holes we define them as the spaces strictly between the rationals
and call the reals complete and continuous.

Additive exponentiation becomes deprecated due to multiplication, but
multiplicative exponentiation still means 'how many' elements are being
composited rather than 'how much' of some effect to apply. Geometry and
algebra conspire to create (or discover) a polar notation way to
describe newly discovered (or invented) complex numbers making use of
imaginary numbers and a 'how much' interpretation of exponentials.

The reals get named as such to distinguish them from the imaginary
numbers used in the complex plane.

Zero and one are fundamental building blocks, and there is no 'problem'
concerning them. There is a perceived problem though when students
think that Calculus only approximates answers due to the problem with
zero appearing as a denominator in a 'ratio' that need not ever be
calculated at all.

Good luck to you in your endeavor, and thanks for dumping that horrible
math forum in favor of Google Groups -- even though GG sucks compared
to a real NNTP client.

Date Subject Author
9/21/17 mitchrae3323@gmail.com
9/21/17 Markus Klyver
9/21/17 mitchrae3323@gmail.com
9/21/17 Markus Klyver
9/21/17 mitchrae3323@gmail.com
9/22/17 Markus Klyver
9/21/17 FromTheRafters
9/21/17 Conway
9/21/17 FromTheRafters
9/21/17 Conway
9/21/17 Dan Christensen
9/22/17 Conway
9/22/17 Dan Christensen
9/22/17 Conway
9/22/17 Peter Percival
9/22/17 FredJeffries@gmail.com
9/24/17 Peter Percival
9/22/17 Dan Christensen
9/22/17 Conway
9/22/17 mitchrae3323@gmail.com
9/22/17 FromTheRafters
9/22/17 Conway
9/22/17 Peter Percival
9/22/17 FromTheRafters
9/22/17 Conway
9/22/17 FromTheRafters
9/22/17 Conway
9/22/17 FromTheRafters
9/22/17 Markus Klyver
9/22/17 FromTheRafters
9/22/17 Peter Percival
9/21/17 mitchrae3323@gmail.com
9/21/17 FromTheRafters
9/21/17 conway
9/21/17 mitchrae3323@gmail.com
9/22/17 Conway
9/22/17 mitchrae3323@gmail.com
9/22/17 Conway
9/22/17 mitchrae3323@gmail.com
9/22/17 Bill
9/22/17 Conway
9/22/17 zelos.malum@gmail.com
9/22/17 Markus Klyver
9/22/17 Markus Klyver
9/22/17 FromTheRafters
9/22/17 Conway
9/22/17 Peter Percival