/sci/ - Science & Math

>>6525044

Because "one" is a unit quantity.

>>6525047

>unit quantity
>unit-y
>unity

Is this some sort of mathematics joke?

I think you should open a dictionary and look up unity. If you still don't get it you may be retarded.

>>6525076
there's no such thing as a mathematics joke.

Why was six afraid of seven?

>>6525044
http://dictionary.reference.com/browse/unity

Personally I prefer "identity".

>>6525096
because 1 is referred to as unity

>>6525100
but 0 is identity too

>>6525100
you run into issues with that in vector spaces and group theory. 1 is multiplicative identity but is not additive identity

>>6525044
>Why is the number 1 sometimes referred to as "unity"?
Actually, there is a reason.

"One" is just a number or a value like any other.
But "unity" has more significance.

For example, the estimated digit of a measured quantity can be the number "one"; no one ever says that a significant digit of a measurement is "unity."
But we say that probabilities add up to "unity". Here, the sum of the probabilities doesn't just happen to be 1; the fact that it is 1 is an important mathematical fact (or definition, rather). Hence, we say that the probabilities add up to "unity"; and the trace of a density matrix in QM is "unity"; and a unital ring's "unit" isn't something that has the value of 1, but rather something with a significant set of properties.

>>6525117

So "unity" refers to the idea of 1, as an identity, rather than 1 as a numerical value?

>>6525105
>>6525102
Of course, I should've specified. I refer to it as the multiplicative identity. The reason I said it was because some of the professors at my university call them the additive unity and multiplicative unity.

>>6525044

In a ring, the identity element for addition is usually denoted 0. If the multiplication has an identity, it's usually denoted 1 and is called the unity element. The ring is then called a "ring with unity". It's just a convention some people use.