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Not quite... numbers are a strange breed. They don't actually describe anything in a way that can be visualized. One could say that they are distances on a number line- but from what? Zero? Remember, the development of mathematics began prior to the actual use of zero- hence, it clearly cannot describe distances from zero. So, if we were to pick a simple number- one, in this case- what could we say it is? It clearly isn't tangible, and it doesn't describe anything in particular... So what is one? Or any other number, for that matter? Now, the actual concept of numbers themselves, at least from what I can tell, arises from something more simple than even that. There are a few basic rules that developed into the nature of mathematics that we know today:
1. The nature of "mathematics" consists of a series of one-dimensional entities.
2. These entities are unique- no two entities occupy the same one-dimensional space.
3. These entities are constant- identical operations with identical numbers will yield identical results.
4. The one-dimensional space of which these entities occupy is a complete metric space.
With that, we could describe the number one as a description of a location within a one-dimensional space. If anything, one isn't a description- it is a definition.
And how does anything here have to relate to the use of "one and one" versus "one plus one?" Simple- the former applies to physical objects, while the latter applies to numbers. After all, the former is a description while the latter is a definition.
1. The nature of "mathematics" consists of a series of one-dimensional entities.
2. These entities are unique- no two entities occupy the same one-dimensional space.
3. These entities are constant- identical operations with identical numbers will yield identical results.
4. The one-dimensional space of which these entities occupy is a complete metric space.
With that, we could describe the number one as a description of a location within a one-dimensional space. If anything, one isn't a description- it is a definition.
And how does anything here have to relate to the use of "one and one" versus "one plus one?" Simple- the former applies to physical objects, while the latter applies to numbers. After all, the former is a description while the latter is a definition.
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The "and" operator is well defined for all types of values, numbers and booleans both included.
The "and" operator in those cases describe, again, a description of a state- on or off. 5 AND 6 would yield 4 due to the nature of binary- but binary itself is a description of a state as either on or off. Hence, the AND operator only works in a single base- binary. Therefore, it cannot be extended to other bases, unlike addition. Therefore, there is clearly a distinction between the two.
You're completely misunderstanding. "and" does not in any way imply "bitwise and". "and" always refers to "+", the name for which is the "plus" symbol.
If I may approach this absurd discussion from another angle,
The answer is "at least one apple", since there's no way of knowing if both apples aren't the same one. But this is irrelevant to the subject at hand. You can rephrase the statement in any number of ways, and it will still have nothing to do with how to read aloud the expression "x + y". For example,
Does this mean we can say "x while y", or "x as y"? No, it doesn't, because "x + y" is not a statement.
I personally have never seen the word "y" used instead of "más", and the RAE doesn't contradict me (http://lema.rae.es/drae/?val=y ). However, what with Spanish being the second most spoken language, it wouldn't surprise me if that usage occurred somewhere. Is it right? Is it wrong? It depends on whether you think linguistics should be prescriptive or descriptive. For the layman, more technical usages are irrelevant.
| Q: If I have an apple in my left hand and an apple in my right hand, how many apples do I have in my hands? |
| Q: If I hold an apple in my left hand while holding a different apple in my right hand, how many apples do I have in my hands? |
| Q: If I hold an apple in my left hand as I hold a different apple in my right hand, how many apples do I have in my hands? |
I personally have never seen the word "y" used instead of "más", and the RAE doesn't contradict me (http://lema.rae.es/drae/?val=y ). However, what with Spanish being the second most spoken language, it wouldn't surprise me if that usage occurred somewhere. Is it right? Is it wrong? It depends on whether you think linguistics should be prescriptive or descriptive. For the layman, more technical usages are irrelevant.
I'm done here. When it all comes down to absurdities based upon some people trying to wrap their super-genius brains around standard usage, and arguing against it because their a priori intelligence makes their grasp on the universe and how things work in it greater than anyone else's... then there is no further teaching or learning to be done.
I hope that I someday arrive at the point where I don't need to learn anything more, because I will have become smart enough to figure it all out on my own.
@helios
You were taught correctly, of course. "Más" is the correct way to say it in Spanish. Perhaps the use of "y" is a Norte-Americanism? Or I could just be wrong... :O)
@Computergeek01
You assume implication where there is none. Try re-reading my comment as if I were agreeing with you...
I hope that I someday arrive at the point where I don't need to learn anything more, because I will have become smart enough to figure it all out on my own.
@helios
You were taught correctly, of course. "Más" is the correct way to say it in Spanish. Perhaps the use of "y" is a Norte-Americanism? Or I could just be wrong... :O)
@Computergeek01
You assume implication where there is none. Try re-reading my comment as if I were agreeing with you...
> I personally have never seen the word "y" used instead of "más"
dos y dos son cuatro
cuatro y dos son seis
seis y dos son ocho, y ocho, dieciséis
y ocho, veinticuatro
y ocho, treinta y dos
Ánima vendita me arrodillo en vos
(La farolera, M. E. Walsh)
32 - 12
32 + 87 = 119
1 + 19 = 20
dos y dos son cuatro
cuatro y dos son seis
seis y dos son ocho, y ocho, dieciséis
y ocho, veinticuatro
y ocho, treinta y dos
Ánima vendita me arrodillo en vos
(La farolera, M. E. Walsh)
32 - 12
32 + 87 = 119
1 + 19 = 20
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I remembered correctly that helios was Argentinian. (Yay!)
As for ne555, I've always had the impression he was from Spain, though I can't give any concrete reason why... (His profile would have me believe he is an oscillating circuit working as a programmable timer.)
Alas, ¿quién habla castillano?
/me runs far, far away
As for ne555, I've always had the impression he was from Spain, though I can't give any concrete reason why... (His profile would have me believe he is an oscillating circuit working as a programmable timer.)
Alas, ¿quién habla castillano?
/me runs far, far away
@ Duoas: That wasn't meant to come off as defensive as it did, that topic just puts me in an aggressive mood (I think it's justifiable). I sort of knew what you meant when you said to question the curricula and I wanted to draw some attention to the frustrations I ran into when I did mostly because, as you can see by the hit counter, nobody around here gives a damn. Everything else with the links and ranting was just me venting. Sorry about that.
Ehhh its disgusting...did you know they are removing the revolutionary war 1776 and teaching kids about the united states constitution from "American History" class?
| And how does anything here have to relate to the use of "one and one" versus "one plus one?" Simple- the former applies to physical objects, while the latter applies to numbers. After all, the former is a description while the latter is a definition. |
You seem to be full of.. well, something smelly.
Merriam Webster:
—used to join words or groups of words : added to : plus —used to describe an action that is repeated or that occurs for a long time |
freedictionary.com:
| 1. Together with or along with; in addition to; as well as. Used to connect words, phrases, or clauses that have the same grammatical function in a construction. 2. Added to; plus: Two and two makes four. 3. Used to indicate result: Give the boy a chance, and he might surprise you. 4. Informal To. Used between finite verbs, such as go, come, try, write, or see: try and find it; come and see. See Usage Note at try. 5. Archaic If: and it pleases you. |
Macmillan:
... used in calculations for showing that numbers are added together Two and two is four. ... |
Oxford English:
| ... Used to connect two numbers to indicate that they are being added together: 'six and four make ten' ... |
Who knew? And can apply to numbers?! You know what else is surprising? Plus isn't used only in the context of numbers!
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Ah!
@Computergeek01
'salright.
My youngest step-son was finally diagnosed last December. He has an extreme case of Bipolar disorder plus what, for his age, is called Oppositional Defiant Disorder, all at the sweet, tender age of eleven.
Before we knew what the problem was, even, it was clear he had some serious issues. We were leaning toward ICD-10 because we had been told (several times) he is not bipolar. (We know now it was hard to diagnose because of the severity of his condition -- and the atypical responses he evidenced -- not to mention how young he is.)
I can't tell you the amount of grief the school system has given us over the years. They fought everything we tried to do. And lied through their teeth to us.
We even have a friend of the family who had worked in the administration of special services school board (now retired) and I remember one time we sat down with them to modify his IEP for more appropriate (and costly! I guess) services, and it took two hours to convince them to obey their legal mandate!
But... this is a digression, and has little to do with general education...
@Computergeek01
'salright.
My youngest step-son was finally diagnosed last December. He has an extreme case of Bipolar disorder plus what, for his age, is called Oppositional Defiant Disorder, all at the sweet, tender age of eleven.
Before we knew what the problem was, even, it was clear he had some serious issues. We were leaning toward ICD-10 because we had been told (several times) he is not bipolar. (We know now it was hard to diagnose because of the severity of his condition -- and the atypical responses he evidenced -- not to mention how young he is.)
I can't tell you the amount of grief the school system has given us over the years. They fought everything we tried to do. And lied through their teeth to us.
We even have a friend of the family who had worked in the administration of special services school board (now retired) and I remember one time we sat down with them to modify his IEP for more appropriate (and costly! I guess) services, and it took two hours to convince them to obey their legal mandate!
But... this is a digression, and has little to do with general education...
Topic archived. No new replies allowed.
Pages: 12