What does one solution mean in math? An equation may have zero, one, or more solutions (this is also true for a system of equations). The equation 2 + x = 5 has only solution, for example. x can only equal 3, so there is one solution. (An example of an equation with more that...
What does the term infinitely many mean in math? For what value of x, is the rational expression below equal to zero? {2 - x} / {2 + x}. For what value of x is the rational expression equal to zero? 20+ \frac{2x}{5-x} ...
If we perform a linear rescaling around the axis of the fat tube by a factor of to turn it into a tube, this would inflate the thin tubes to be rescaled tubes of dimensions , which would now be -separated in direction. This rescaling does not affect the multiplicity of the tubes. ...
Chaos theory is a branch of mathematics that studies the consequences of nonlinearity in natural phenomena. It is broadly concerned with how systems that are sensitive to the initial conditions behave. Therefore, it can be difficult to predict what will happen over time, even if the system only...
12:58 Isn’t the illuminated portion of the Moon, as well as the visible portion of the Moon, slightly smaller than half of the entire Moon, because the Earth and Sun are not an infinite distance away from the Moon?Technically yes (and this is actually for a very similar reason to why...
Here’s a snippet of GPT-4’s response: “If we take the smallest number in S that is not in P / And call it p, we can add it to our set, don’t you see? / But this process can be repeated indefinitely. / Thus, our set P must also be infinite, you’ll agree.” ...
What Does It Mean If Demand Is Perfectly Inelastic? Demand is said to be "perfectly inelastic" if the demand for that product will remain consistent, regardless of any price changes. Perfectly inelastic demand occurs rarely in the real world. Close examples might include rare medicines, or fresh...
The field of “BERTology” aims to locate linguistic representations in large language models (LLMs). These have commonly been interpreted as rep
In mathematics, what does it mean for two things to be the same? The equal sign first appeared in 1557 in Robert Recorde's work "The whetstone of Witte". The principle of indiscernity of identicals says that equal things have the same properties. If two things were literally exactly the...
You're putting an approximation into an infinite series of terms. What I'm doing is replacing one real number by another slightly smaller real number, where the numbers were so small to begin with that the difference between them doesn't matter. The infinite series [itex] x_1 = x_0 ...