Limit Quotes - page 27
Take the case of the infinite ocean. There is no limit to its water. Suppose a pot is immersed in it: there is water both inside and outside the pot. The jnani sees that both inside and outside there is nothing but Paramatman. Then what is this pot? It is "I-consciousness". Because of the pot the water appears to be divided into two parts; because of the pot you seem to perceive an inside and an outside. One feels that way as long as this pot of "I" exists. When the "I" disappears, what is remains. That cannot be described in words.
Ramakrishna
Röntgen has familiarized us with an order of vibrations of extreme minuteness compared with the smallest waves with which we have hitherto been acquainted, and of dimensions comparable with the distances between the centers of the atoms of which the material universe is built up; and there is no reason to suppose that we have here reached the limit of frequency.
William Crookes
Many people believe that they were made by their parents: 'I didn't ask to be born.' they cry. This is completely wrong. Please try to remember when your were five. If you try then you will remember that this memory had no beginning. It seems as if you can remember living infinitely; that your life didn't begin when you were born but continues without limit.
Michio Kushi
In a clean break from the Obama years, and frankly from the years before this president, we will keep federal spending at 20 percent of GDP, or less. That is enough. The choice is whether to put hard limits on economic growth, or hard limits on the size of government, and we choose to limit government.
Paul Ryan
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
