Add Quotes - page 32
It takes these very simple-minded instructions - 'Go fetch a number, add it to this number, put the result there, perceive if it's greater than this other number' - but executes them at a rate of, let's say, 1,000,000 per second. At 1,000,000 per second, the results appear to be magic.
Steve Jobs
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
!-- A motion was made and seconded, that the report of the Committee made on Monday last, be amended, so far as to add the following to the first article therein mentioned, viz.: ' -->And that the said Constitution be never construed to authorize Congress to infringe the just liberty of time press, or the rights of conscience; or to prevent the people of the United States, who are peaceable citizens, from keeping their own arms; or to raise standing armies, unless when necessary for the defence of the United States, or of some one or more of them; or to prevent the people from petitioning, in a peaceable and orderly manner, the federal legislature, for a redress of grievances; or to subject the people to unreasonable searches and seizures of their persons, papers or possessions.
Samuel Adams