Re: Interesting math

Purl Gurl filted:

By convention, we also define a number as even if
divisible by an even number with no remainder,
this is, modulus zero.

So far, so good....

By convention, we also define a number as odd if
divisible by an odd number with no remainder,
this is, modulus zero.

Er, no, we don't do that at all....

10 / 2 = 5 (ten is even, modulus zero)
15 / 3 = 5 (fifteen is odd, modulus zero)

0 / 2 = 0 (zero is even, modulus zero)
0 / 3 = 0 (zero is odd, modulus zero)

6 / 3 = 2 (no remainder; by your "convention", this makes six an odd number)....

An enjoyable convention,

Well, I'm glad *someone's* enjoying it....

By convention, we also define a number as even if
divisible by an odd number producing an even
resultant with no remainder, this is, modulus zero.

Which is the same as the "divisible by an even number" definition...you just
moved the factor of two from the divisor to the quotient....

Yet another convention,

By convention, we also define a number as even
if a multiple of two.

Which is just another way of stating that it's divisible by two....

There you have your convention and a number of other
conventions. Those conventions are contradictory.

Only that squirrely one about a number being odd if it's divisible by an odd
number...the others get along just fine....

Now what?

Now we go back to how "even" and "odd" are *really* defined:

1) A number is "even" if dividing it by two produces no remainder
2) A number is "odd" if dividing it by two produces a remainder
Corollary: no number can be both odd and even

(All the above, of course, assumes that "number" means "integer"...the number
1.618 is neither odd nor even)....

Here is a very interesting example.

0 / 0 = 0

We accept division by zero is undefined yet this
example well establishes division by zero is defined.

Except that it's not true...the rules of arithmetic declare a certain number of
"indeterminate forms", of which 0/0 is one...others are n/0 (where n is a
non-zero value) and infinity-infinity....

Just because you can write "0/0=0" doesn't make it so...I can write "2+2=37", or
"8/4=banana", and in fact I just did...the world did not benefit appreciably
from the effort....r


--
"You got Schadenfreude on my Weltanschauung!"
"You got Weltanschauung in my Schadenfreude!"
.

Relevant Pages

  • Re: Interesting math
    ... So 0 is not odd. ... divisible by an even number with no remainder, ... this is, modulus zero. ... An enjoyable convention, ...
    (alt.usage.english)
  • Re: Interesting math
    ... divisible by an even number with no remainder, ... this is, modulus zero. ... divisible by an odd number with no remainder, ... An enjoyable convention, ...
    (alt.usage.english)
  • Re: Interesting math
    ... R H Draney wrote: ... By convention, we also define a number as even if ... divisible by an even number with no remainder, ... this is, modulus zero. ...
    (alt.usage.english)
  • Re: Interesting math
    ... divisible by an odd number with no remainder, ... this is, modulus zero. ... No prime number can be odd. ... know how computer-science types talk about recursive algorithms ...
    (alt.usage.english)
  • Re: Interesting math
    ... By convention, we also define a number as even if ... divisible by an even number with no remainder, ... we also define a number as odd if ... A definition closer to reality is this: ...
    (alt.usage.english)