# Questions tagged [definition]

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### Peano's question about how to define a definition

In Wikipedia’s Peano entry I find the following quote: [In] the First International Conference of Philosophy [Peano] presented a paper which posed the question of correctly formed definitions in ...
280 views

### What's the difference between Galileo's "impeto" and "momento"?

In Galileo's Two New Sciences, he describes an experiment demonstrating pendulum motion and how the pendulum will rise to the same height from where it started its fall. This discussion can be found ...
1 vote
102 views

### Definition and Name Change of the Oscillation Function

I have two related questions: Who first defined the oscillation function (perhaps under a different name)? When did the switch from the phrase "saltus function"(*) to "oscillation ...
1 vote
178 views

### What is the difference between Newton's definitions and axioms?

What is the difference between definition and axiom? For instance, Newton's Definition 1 reads: (Cohen p. 403) Quantity of matter is a measure of matter that arises from its density and volume ...
118 views

### Examples of mathematical definitions motivated by engineering problems

I'm interested in the development of mathematical definitions for the sake of engineering, and what makes a particular definition better suited for a problem than another in any particular context. ...
85 views

### What does P. G. Tait mean by "double points"?

I am reading the following short paper: P. G. Tait. Some elementary properties of closed plane curves. Messenger (2) 6 (1877), 132–133. JFM 09.0393.01 Here, Tait writes The closed curves ...
165 views

### Why did the mathematical community settle on these properties to define a topology?

The following post is long, but I decided to write more rather than less in case it's helpful. I tried to make it clear, quick, and easy to skip to the short version of my question, so the reader can ...
149 views

### Motivation behind original definition of metre? [duplicate]

The first original definition of the metre, presented by the French Academy of Sciences in 1795 is: The length of the metre is one ten-millionth of the Earth quadrant, the distance from the North ...
245 views

### History of the definition of complex derivative

Almost all of modern complex analysis (Cauchy residue theorem, analytic continuation, etc) depend on the definition of a complex derivative. That definition requires the derivative at a point $z_0$ is ...
176 views

### When were equivalence classes formalized?

Neither wikipedia or the first few pages of Google are showing me much about the history of the development of equivalence classes. When was this notion first formalized? Footnote: I originally asked ...
The ordinal multiplication $\cdot$ can be defined recursively via ordinal addition $+$ for any ordinal $\alpha$ as follows: $\alpha\cdot 0=0$. $\alpha\cdot (\beta+1)=\alpha\cdot \beta+\alpha$ for any ...