By G. Birkhoff (ed.)
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My father had made that decision without discussing it with any of us. We had liked living in the city, taking the buses, walking to the stores. But we had no choice. So we moved to the county. There I attended an all-black school from the fifth through the eighth grades. White neighborhoods were right next to Negro neighborhoods, but blockades separated the ends of the streets, and there were separate schools. Angela Mae Kupenda I attended West Side Elementary and Junior High School. For a while, my family members were “big shots” because we were from the city, made good grades, and lived in a brand-new three-bedroom, two-bath home.
Sometimes the commutative property holds and sometimes it doesn’t. Order matters in subtraction and division but not in addition or multiplication. The concept seems so basic that it is not worthy of study. ” The theoretical foundations of elementary arithmetic turn out to be very, very difficult, well beyond, let me assure you, that wall of theoretical mathematics that I hit long ago at Ohio State. I cannot explain why the commutative property does not apply to subtraction, nor can I understand the proof when it is set before me.
He told me that all the Elizabeth Islands were criss-crossed with these wonderful, elegant stone walls that carved the islands from rocky shore to smooth beaches, through sheep grazing fields and across scrub pine and oak. There are no paved roads on any of these islands even today; then, there were sheepherders and there were horses, but very few houses and buildings. My father pointed out these wonderful rocky walls and asked whether I noticed something different about them—different than what I noticed about the rest of the island.
Orbit Theory: Proceedings by G. Birkhoff (ed.)