"Evenly even" and "evenly odd" are old mathematics terms meaning, respectively, if I remember correctly, giving an even or an odd number when divisible by two. These definitions need to be confirmed. -- Paul G 14:50, 15 Apr 2004 (UTC)
- Confirmed, sort of. These terms are older and I can't track down an authorative reference. Mathworld uses "doubly even" for "evenly even" and I would think modern mathematicians would tend to recast in terms of remainder mod 4.
- One random source on the web (http://www.domcentral.org/study/ashley/arts/arts301.htm) gives these definitions:
- Evenly even: 0 mod 4 (4, 8, 12, 16 ...)
- Oddly even: 2 mod 4 (2, 6, 10, 14 ...)
- Evenly odd: (2n + 1)2^k, or basically every even number not a power of 2 (6, 10, 12, 14, 18 ...).
- But another random source (http://www.bendigo.latrobe.edu.au/sae/arts/tradcosmos/maths1.html) gives "Evenly even" and "evenly odd" as you have above.
- In any case, these usages seem to belong more to numerology than mathematics, though they were once considered mathematical terms (and for that matter, mathematics and numerology used to have much more overlap). -dmh 15:27, 15 Apr 2004 (UTC)
Usage note on Etymology 2
Yesterday I added the following note on usage to the second "etymology":
- Usage note: Sometimes even is used rather in the opposite way to the above. For instance, it is proper to say "I didn't even make it through the front door", but one also hears:
- Did you even make it through the front door?
- Here making it through the front door is thought of as a minimal accomplishment, not a maximal one.
- The word even is often placed in what is technically the wrong place: "Assuming the perpetrator can even be found, such cases often hinge entirely on personal testimony" (New Scientist, 12 July, 2014, p. 16) instead of "Even if the perpetrator can be found...". Or:
- That was before I was even born.
- instead of "That was even before I was born".
This was immediately reverted by a user named user:Kephir, who objects to what I wrote, as well as to the formatting. I would like to defend what I said. As for the formatting, that is certainly not grounds for reverting!
If someone was planning to go into the headquarters of some corporation and throw a pie into the face of the CEO, one might ask him afterwards, "Did you even throw the pie into his face?" That would be correct usage. It's a question corresponding to the statement "I even threw the pie into his face." But to ask "Did you even get in the front door?" is the opposite. It corresponds to the statement "I didn't even get in the front door." I wonder whether Kephir sees the difference between the two questions.
In other languages I know, the second question would not use the same word to translate "even" as in the first question. For instance, in French, one would not say, "Est-ce que tu as même réussi à entrer dans le batiment?"
The other two examples I gave are not so much examples of using the word "even" when it shouldn't be used, but of putting it in the wrong place. (Note that I am using the word "wrong" here for simplicity, not because I'm trying to make people conform to what I think is right.) For instance, in the example with "perpetrator", the sentence is not saying "Assuming that the perpetrator is not only identified, but even found...". It is saying, "Even if one assumes that the perpetrator is found...". And in the example with "born", what is extreme is the point in time, not the birth. So technically the "even" should go before "before". Again, look at how this would be said in other languages. You wouldn't say "C'était avant que je sois même né", you would say "C'était même avant que je sois né'.