What is the hypotheses of the mean value theorem? Is functional analysis used in machine learning? Is surveying a real-life example where radical expression might be used? Bonus: Explain the significance of the mean value theorem. What does it imply? What does epsilon mean in math? Explain t...
What does epsilon mean in math? What does the symbol ^ mean in mathematical expressions and functions? What does ellipsis mean in math? Explain what is algebra and give an example. What does an apostrophe mean in math? In math, what does algorithm mean? Give an example to explain the bas...
Epsilon-delta is the definition of a limit. All those handy rules you learned were derived from epsilon-delta arguments. It's somewhat important. They were derived that way in the sense that someone did it that way (Weierstrass or Cauchy or someone like that), but they were not INVENTED...
What does interior mean in math? Vocabulary in Math: Vocabulary terms in mathematics can be tricky. The terms and words used in mathematics can sometimes have a different meaning than those same terms and words in everyday language, but they can also sometimes mean the same thing. Thus, bein...
“compact” in various senses, which is particularly useful in being able to upgrade qualitative (or “pointwise”) bounds to quantitative (or “uniform”) bounds, more or less “for free”, thus reducing significantly the burden of “epsilon management” (although the price one pays for this...
Setting = (/2)-p to the largest of the bounds in (2) above, we can say that when a real number is rounded to the closest floating-point number, the relative error is always bounded by e, which is referred to as machine epsilon. ...
When interpreted in a finitary setting, this concept requires a fair amount of “epsilon management” to manipulate; also, Walsh’s argument uses some other epsilon-intensive finitary arguments, such as a decomposition lemma of Gowers based on the Hahn-Banach theorem. As such, I was tempted to...
This factor is called the wobble.Setting ε = (β/2)β-p to the largest of the bounds in (2) above, we can say that when a real number is rounded to the closest floating-point number, the relative error is always bounded by ε, which is referred to as machine epsilon. In the ...
That we are controlling the size of the epsilon neighborhood, and the choice of epsilon is made so that the neighborhoods do not overlap. (F2-3 relates to I2-2 and I2-3). (3) The contradictions are the same, i.e., that eventually, terms in the sequence are in two places at once...
I tried to get my head around the covariant and contravariant parts. Of course I know what this means in general, but what does it mean here? How is it related? Is there a natural way how the ##V's## come up contravariant and the ## V^{*'}s## covariant? Without coordinate tran...