>>41
ln(1) is the power to which e would need to be represented in order to equal 1.
but
log base sqrt(1) of 1, i.e. the power to which sqrt(1) would need to be represented in order to equal 1, would be defined and not 0, and you can use any base log for that division.
>>50
Incorrect numbering. it is meant to be 1.999... and 1.111...
the '...' represent the endless number series
Name:
Anonymous2006-04-06 18:17
Let A be an algebra where:
1 and 3 are constant symbols
+ is a binop symbol
1+1=3 is an axiom
An infinite number of such algebras can be constructed.
Name:
Anonymous2006-04-07 3:59
>>52
Yes, they can, but to anyone but the maker of the algebra would see it as gibberish and the effort would be moot.
If 1 + 1 = 3 then 1 = 1.5, and since 1 = 1, then 1 != 1.5. Therefore, 1 + 1 != 3
Name:
Anonymous2006-04-07 5:04
1=0, 0=1, there is no 2, without 2 there is no 3
Name:
Anonymous2006-04-07 6:42
but 1 obviously does not = 0, because 1 is something, and 0 is nothing
>>53
he's saying something like, pretend 3 is the new 2, and 2 is the new three,
1 + 3 = 2
1 + 2 = 4
3 + 2 = 5
he's just pointing out the only way to really ever prove 1 = 2 would require changing the way we intepret the numbers.
Name:
Anonymous2006-04-07 12:26
it's called proof by contradiction, by making a stupid assumption, and showing how stupid the assumption is, therfore falsifying it.
>>15
Your use of sets is clearly flawed.
You haven't studied the great fluicity of calculus where if
a fuction is in a specific set of numbers there is a limit to which this function gets close to a number outside of it's own set and thus since numbers are themselfs functions of information it is not flawed that the a number cannot achive a number outside of it sets and even if two numbers of the same function in the same number set cannot achive a number outside of it's set. Thus, you should study the physics of how numbers can formulate in this real plane that we live in.