Wikipedia:Reference desk/Archives/Mathematics/2007 January 26

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[edit] January 26

[edit] 3+1=3

I know that there is a mathematical formula for this problem (3+1=3) but i cant seem to find it anywhere on the internet. If you would be as kind as to help me, my e-mail address is <email removed>. Thanks 165.29.120.18 20:46, 26 January 2007 (UTC)Kelsey

3+1=4. Honestly.87.102.5.92 22:13, 26 January 2007 (UTC)
3+1 is 4. However, it may be some sort of puzzle, a (bad) example being 1+1=11. And rather impolite to ask a public question expecting a private answer... -74.105.234.51 22:32, 26 January 2007 (UTC)
You might want to check out the Invalid_proof page, which has several mathematical "proofs". The statement "3+1=3" can probably be "proven" in the same way as one of the others. Seth Terashima 23:44, 26 January 2007 (UTC)

Sorry to get here so late, but here's a proof for you:

Starting from Peano's axioms: The natural numbers consist of a set N together with a "successor function" f() such that:

  1. There exist a unique member of \mathbb{N}, called "1", such that f is a bijection from \mathbb{N}-{1} to \mathbb{N}.
  2. If a set, \mathbb{X}, contains 1 and, whenever it contains a member, n, of \mathbb{N}, it also contains f(n), then \mathbb{X}= \mathbb{N}. (This is "induction")

We then define "+" by: a+1= f(a). If b is not 1 then b= f(c) for some c and a+b is defined as f(a+c).

Since 2 is DEFINED as f(1), it follows that 2= f(1)= 1+ 1.

In 2+ 2 = 4. We DEFINE 3 as f(2) and 4 as f(3). 2=f(1) so 2+2= f(2+1). But 2+1= f(2)= 3 so 2+2= f(3)= 4! [Mαc Δαvιs] X (How's my driving?) ❖ 17:58, 31 January 2007 (UTC)

[edit] Confidence interval

Dear Expert, For the purpose of publication, I have used regression analyses and amongst different factors, one of the factors had Odds ratio of 1.02 and p-value of 0.02 and Confidence interval was 1.02-1.15 (small but significant effect?). The reviewer has asked me to explain "What is the purpose of Confidence Interval for that factor?" He has not asked the same question about other factors. Could you please help me to understand what is important about this CI? many thanks —The preceding unsigned comment was added by Arafzal (talk • contribs) 21:23, 26 January 2007 (UTC).

A confidence interval is a measure of the uncertainty associated with estimating the value of a population parameter from the data in a sample of that polulation. In other words, you have estimated a value a for a factor or parameter based on your sample data, but you are also saying that with probability p (usually 90% or 95%) the actual population value lies between b and c. Your confidence interval is b-c with probability p. The reviewer is probably suggesting that your paper should include an explanation of what the "confidence interval" that you have quoted actually means in the context of your analysis - just telling the reader that it is a confidence interval is too vague. If you have used a statistical package to calculate your values then you may need to find out more about the calculations and methods that the package is actually using. Gandalf61 09:19, 28 January 2007 (UTC)