Paraconsistent logic does not allow contradictions; it does not allow (A & ~A) to be true. — Banno
a certain way of talking about the world is found in many places. There are, after all, languages without much by way of number. Would you say that the folk who speak them have failed to notice an aspect of reality, or would you say that they have no use for a particular process, a certain way of speaking? — Banno
I'm not being snide. It is a genuine issue amongst mathematics teachers. See the Wiki article on 0.99... It's on a par with kids who are not able to see three dots as three.
Folk who think 0.99...<>1 have missed a vital aspect of mathematics. — Banno
Life is too short — Olivier5
I tend to find SEP unreliable — Olivier5
it approaches 1, but it never quite does become 1, though, does it? — Janus
...instantiate... — Janus
who would not be able to see that three dots are three? — Janus
Are you going to make a cogent argument as to how a series that is approaching one and could do so forever without actually reaching it is the "very same as I" — Janus
paraconsistent systems avoid inconsistency by redefining it as other than (A & ~A), usually by adding a third truth value. — Banno
t is impossible to instantiate an infinite series — Janus
A set S of formulas is inconsistent iff there is a formula P such that both P and ~P are members of S. — TonesInDeepFreeze
(SEP)The role often played by the notion of consistency in orthodox logics, namely, the most basic requirement that any theory must meet, is relaxed to the notion of coherence:... Simple consistency of a theory (no contradictions) is a special case of absolute consistency, or non-triviality (not every sentence is a part of the theory).
Here's an instantiated infinite series for you:
1,2,3... — Banno
You misread it.
As I said, it's an issue of pedagogy. You need learnin'.
(the bit where I said I wan't going to do this...!) — Banno
if you added .9, .09, .009, .0009. .00009, and so on forever — Janus
By "instantiate an infinite series" I mean write it down as a full series, not in a shorthand form. I'm no mathematician, but that logical distinction is clear. — Janus
The word 'instantiate' has a certain meaning in mathematics. What you mean though - to type out in finite time and space individually all the members of an infinite set - is of course impossible. But that doesn't entail that the limit of an infinite sequence is not rigorously defined. — TonesInDeepFreeze
there can be no actual infinite quantities of anything. — Janus
it seems we are not disagreeing about anything — Janus
Of course, if one doesn't countenance infinite sets, then one might not countenance the classical notion of convergence to a limit. But that doesn't change that what ordinary mathematics mean by '.999...' is not some kind of "reaching" but rather convergence to a limit — TonesInDeepFreeze
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