Register to reply 
Origin of numbers 
Share this thread: 
#1
Apr505, 11:25 AM

PF Gold
P: 2,938

In the "origin of zero" thread, I saw the following remark:



#2
Apr505, 11:39 AM

Sci Advisor
HW Helper
P: 9,396

Do you mean mathematical origin or philosophical origin?



#3
Apr505, 12:59 PM

Sci Advisor
HW Helper
P: 1,123

If you can try and find a book called 'Surreal Numbers' by Donald Knuth. Very enlightening about the importance of what some refer to as 'trivial' properties of numbers.



#4
Apr505, 04:01 PM

Sci Advisor
HW Helper
P: 9,499

Origin of numbers
or cultural origin, or geographical origin, or temporal origin?



#5
Apr605, 04:53 AM

PF Gold
P: 2,330

Also, if an even number is a number which can be divided into equal parts, and an odd number is a number which is not even, then unity is an odd number, as it cannot be divided into equal parts. I can't think of a definition of oddness which excludes unity without using it. Let x and y be individual variables ranging over set S. Say x is even if there exists some y such that (y + y = x). How will you define oddness? 


#6
Apr605, 09:32 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,682

I would define "smallest even number" (of a given set of integers) as the even number, x, in the set such that if y is any even number in the set, then x is less than or equal to y. That doesn't use "unity".
The problem I have with arivero's "...ie if it can be divided or not in equal parts. From this we get the smallest odd quantity, 3, and the smallest even, 2. The unity is not got because it can not be divided after all." (I assume he meant "at all") is that saying "a number is odd if it cannot be divided in equal parts" certainly does apply to 1. If it cannot be divided at all, then it certainly cannot be divided in equal parts and so is odd. 


#7
Apr1605, 01:34 PM

P: 1,373

Math is devised into quantities...and from a psychological standpoint the first quantity you recognize is 1.



Register to reply 
Related Discussions  
Irrational numbers vs. Transcendental numbers  General Math  10  
A new set of numbers as a zAxis to imaginary and real numbers?  General Math  9  
Line of real numberstranscendental numbers  General Math  11  
Irrational numbers depends on rational numbers existence  General Math  0 