A Quote by Niels Henrik Abel
Until now the theory of infinite series in general has been very badly grounded. One applies all the operations to infinite series as if they were finite; but is that permissible? I think not. Where is it demonstrated that one obtains the differential of an infinite series by taking the differential of each term? Nothing is easier than to give instances where this is not so.
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In the order of literature, as in others, there is no act that is not the coronation of an infinite series of causes and the source of an infinite series of effects.
The difficulties in the study of the infinite arise because we attempt, with our finite minds, to discuss the infinite, assigning to it those properties which we give to the finite and limited; but this... is wrong, for we cannot speak of infinite quantities as being the one greater or less than or equal to another.
The Infinite alone exists and is Real; the finite is passing and false. The Original Whim in the Beyond caused the apparent descent of the Infinite into the realm of the seeming finite. This is the Divine Mystery and Divine Game in which Infinite Consciousness for ever plays on all levels of finite consciousness.
With the exception of the geometrical series, there does not exist in all of mathematics a single infinite series the sum of which has been rigorously determined. In other words, the things which are the most important in mathematics are also those which have the least foundation.
I know not how to express better, what my sins appear to me to be, than by heaping infinite upon infinite, and multiplying infinite by infinite . . . When I look into my heart and take a view of my wickedness, it looks like an abyss infinitely deeper than hell.
Mathematics has been called the science of the infinite. Indeed, the mathematician invents finite constructions by which questions are decided that by their very nature refer to the infinite. This is his glory.
Don't look back—forward, infinite energy, infinite enthusiasm, infinite daring, and infinite patience—then alone can great deeds be accomplished.
There is no doubt that we cannot do without variable quantities in the sense of the potential infinite. But from this very fact the necessity of the actual infinite can be demonstrated.
Today I said to the calculus students, "I know, you're looking at this series and you don't see what I'm warning you about. You look and it and you think, 'I trust this series. I would take candy from this series. I would get in a car with this series.' But I'm going to warn you, this series is out to get you. Always remember: The harmonic series diverges. Never forget it."
Notable enough, however, are the controversies over the series 1 - 1 + 1 - 1 + 1 - ... whose sum was given by Leibniz as 1/2, although others disagree. ... Understanding of this question is to be sought in the word "sum"; this idea, if thus conceived - namely, the sum of a series is said to be that quantity to which it is brought closer as more terms of the series are taken - has relevance only for convergent series, and we should in general give up the idea of sum for divergent series.
Every single person has within an ocean of pure vibrant consciousness. Every single human being can experience that - infinite intelligence, infinite creativity, infinite happiness, infinite energy, infinite dynamic peace.
In this external world, which is full of finite things, it is impossible to see and find the Infinite. The Infinite must be sought in that alone which is infinite, and the only thing infinite about us is that which is within us, our own soul. Neither the body, nor the mind, nor even our thoughts, nor the world we see around us, is infinite.
There's always going to be one more thing. Because that's what infinite feels like. And the difference between love and everything else is that it's infinite, it's built out of something infinite, or it feels like it is, anyway, which is the same thing to us. You think a million billion more things will come your way, a million billion more versions of everything. But no, everything that actually causes that infinite feeling, the circumstances of every infinite feeling, is so, so finite.
Even as the finite encloses an infinite series
And in the unlimited limits appear,
So the soul of immensity dwells in minutia
And in the narrowest limits no limit in here.
What joy to discern the minute in infinity!
The vast to perceive in the small, what divinity!
God is Infinite and His Shadow is also infinite. The Shadow of God is the Infinite Space that accommodates the infinite Gross Sphere which, with its occurrences of millions of universes, within and without the ranges of men's knowledge, is the Creation that issued from the Point of Finiteness in the infinite Existence that is God.
I have been in the series for over 3 years - 3 series. There will be a fourth series next year which of course I won't be in because I'm now dead. So in total I appeared in 25 episodes.
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