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See lessIrrationality of the constant e of exponential function.
What you should be teaching your students is not that "the sum of rational numbers is rational", but, "the sum of two rational numbers is rational" which you can extend, using the principle of mathematical induction, to "the sum of a *finite* number of rational numbers is rational". It should be cleRead more
What you should be teaching your students is not that “the sum of rational numbers is rational”, but, “the sum of two rational numbers is rational” which you can extend, using the principle of mathematical induction, to “the sum of a *finite* number of rational numbers is rational”.
It should be clear that this claim cannot be extended to *infinite* sums blindly. In fact, by definition, an infinite sum is actually the limit of a finite sum (partial sums).
“e” is a counterexample for this. The infinite sum of rational numbers need not necessarily be a rational number.
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See lessSearching for Easy Tip
There is a webinar on the number Pi tomorrow (14th) at 6 pm where these topics will be touched. We invite you to join that. The link is on the home page on MetaHub. https://learn.zoom.us/j/63881167775?pwd=YU5WeFFLcFJOM3M0NDhNUFB3Wk54QT09 We'll wait to see what other teachers have to say on this (whaRead more
There is a webinar on the number Pi tomorrow (14th) at 6 pm where these topics will be touched. We invite you to join that. The link is on the home page on MetaHub.
https://learn.zoom.us/j/63881167775?pwd=YU5WeFFLcFJOM3M0NDhNUFB3Wk54QT09
We’ll wait to see what other teachers have to say on this (what techniques they use) and our reply will be posted in a few days time.
See lessFunctions
Codomain Y is a set stated by the definition of a function such that all outputs of the function need to be within it , in other words it is a set of all possible outputs. Range R is the set of all outputs of a function and which can be determined by the relation and domain of the function. ThereforRead more
Codomain Y is a set stated by the definition of a function such that all outputs of the function need to be within it , in other words it is a set of all possible outputs. Range R is the set of all outputs of a function and which can be determined by the relation and domain of the function. Therefore by definition R should be a subset of Y. If R = Y function maps it’s domain onto codomain , if R ⊂ Y function maps it’s domain into codomain.
To get a better insight of the issue we can consider probability function because it has practical importance and we can clearly see the difference of the two sets . Here the domain is Event space and codomain is the set [0,1] but range is only particular values within the set [0,1]. In the case of tossing a coin once range is the set {0,1/2 , 1} .
See lessReal number system
Here you have the related informations, your suggestions are greatly appreciated.
Here you have the related informations, your suggestions are greatly appreciated.
See lessIllustrating powers of sums by geometrical means
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Here you have related informations, your suggestions are greatly appreciated.
See lessDivisors and factors
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Here you have the related informations, your suggestions are greatly appreciated.
See lessTimes table
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Here you have related informations , your suggestions are greatly appreciated.
See lessParadoxes
Here you have the related informations, open for your suggestions.
Here you have the related informations, open for your suggestions.
See lessConjectures
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Here you have related informations, open for your suggestions.
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