A free abelian group of rank n is isomorphic to ℤ⊕ℤ⊕...⊕ℤ= bigoplus ⁿℤ, where the ring of integers ℤ occurs n times as the summand. The rank of a free abelian group is the cardinality of its basis. The basis of a free abelian group is a subset of it such that any element of it can be expressed as a finite linear combination of elements of such basis, with the coefficients being integers. (For an element a of a free abelian group, 1a = a, 2a = a + a, 3a = a + a + a, etc., and 0a = 0, (−1)a = −a, (−2)a = −a + −a, (−3)a = −a + −a + −a, etc.)

Deflectors say there's something there, sensors say there isn't. Density negative. Radiation negative. Energy negative.

Among the 16 mahajanapadas the monarchical states of Kosala, Vatsa, Avanti, and Magadha, along with the non‐monarchical mahajanapada of the Vrijis or Vajjis, attained political prominence by eclipsing other contemporary powers. However, it was the mahajanapada of Magadha which ultimately rose to prominence.

I'm no good now, I'm burnt out. I was real good but only got one good and one bad one. My leg, look! That's it! But the other leg, she's apples. And that's how it is.