Series Quotes - page 47
When... we have a series of values of a quantity which continually diminish, and in such a way, that name any quantity we may, however small, all the values, after a certain value, are severally less than that quantity, then the symbol by which the values are denoted is said to diminish without limit. And if the series of values increase in succession, so that name any quantity we may, however great, all after a certain point will be greater, then the series is said to increase without limit.
Augustus De Morgan
Take a unit, halve it, halve the result, and so on continually. This gives-1 1⁄2 1⁄4 1⁄8 1⁄16 1⁄32 1⁄64 1⁄128 &c.;Add these together, beginning from the first, namely, add the first two, the first three, the first four, &c;... We see then a continual approach to 2, which is not reached, nor ever will be, for the deficit from 2 is always equal to the last term added.
...We say that-1, 1 + 1⁄2, 1 + 1⁄2 + 1⁄4, 1 + 1⁄2 + 1⁄4 + 1⁄8, &c.; &c.;is a series of quantities which continually approximate to the limit 2. Now the truth is, these several quantities are fixed, and do not approximate to 2. ...it is we ourselves who approximate to 2, by passing from one to another. Similarly when we say, "let x be a quantity which continually approximates to the limit 2," we mean, let us assign different values to x, each nearer to 2 than the preceding, and following such a law that we shall, by continuing our steps sufficiently far, actually find a value for x which shall be as near to 2 as we please.
Augustus De Morgan
The following is exactly what we mean by a LIMIT. ...let the several values of x... bea1 a2 a3 a4.... &c.;then if by passing from a1 to a2, from a2 to a3, &c.;, we continually approach to a certain quantity l [lower case L, for "limit"], so that each of the set differs from l by less than its predecessors; and if, in addition to this, the approach to l is of such a kind, that name any quantity we may, however small, namely z, we shall at last come to a series beginning, say with an, and continuing ad infinitum,an an+1 an+2.... &c.;all the terms of which severally differ from l by less than z: then l is called the limit of x with respect to the supposition in question.
Augustus De Morgan
Mantle played ball almost under a shroud of depression, because he always thought he was going to die an early death. But Mays probably thinks he's going to live forever. Mantle acted like a man who was doomed. Mays never did, even though he played long beyond his ability. I talked to Willie after the 1973 World Series, in which he looked terrible. I said, "What were you doing out there, Willie?" "Oh, I was having fun!" he told me. Mantle never had fun. Mays, on the other hand, seemed to be inoculated from all the pressure. He simply went beyond the usual frames of reference. If I were writing this, I'd say that he went beyond the usual frames of reverence. That's the way we all felt, and I think it was true for not only the press, but also for managers and other players. And this bled into the other pages of the newspaper.
Arnold Hano
I have a whole series of pictures that are, I mean in a sense, landscapes. Well, I wouldn't hold the landscape in front of me and translate it more abstractly into the painting, no. But I would - again in that American expedient thing you [Barbara Rose, earlier in the interview] were talking about - thinking ideas in my language. Sort of like today. 'Hm, bunch of roses', hm. 'Flags out the window', hm.... But once it got down on the surface I would say in 99 times out of a 100, out of 101, nobody would come along and say how come you put 'shoes' in a picture. I mean it would be too brown or too green.
Helen Frankenthaler