For since the fabric of the universe is most perfect and the work of a most wise Creator, nothing at all takes place in the universe in which some rule of maximum or minimum does not appear.
Leonhard EulerRead
To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be.
Interpretation
What this quote means
The quote emphasizes that the concept of an infinitely small quantity in mathematics is fundamentally understood to be zero, dispelling common misconceptions.
Leonhard Euler's quote sheds light on the concept of infinitely small quantities in mathematics, suggesting that what is often perceived as mysterious or complex can actually be simplified to a basic understanding. By stating that these quantities equate to zero, Euler conveys that many mathematical mysteries may not be as complicated as they seem, inviting a deeper exploration of foundational mathematical principles.
Themes
MathematicsZeroInfinitely SmallComplexitySimplification
In practice
Example use cases
In a mathematics class discussing limits and calculus.
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All quotes →After exponential quantities the circular functions, sine and cosine, should be considered because they arise when imaginary quantities are involved in the exponential.
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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.
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