Talk:exponent

Deletion discussion

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exponent

The third and fifth (second and third 'mathematical') senses. Follow-up to this discussion (as I hinted there, I'm not enough of a mathematician to meddle with the entry myself. --Droigheann (talk) 03:43, 20 February 2016 (UTC)

I would leave only the first 'mathematical' sense and delete the other two. They are only exponents in the sense that they represent the same basic relationship (For example $\log _{b}(a)=4$ is equivalent to $b$^$4$$=a$ and $sqrt[2]r=b$ is equivalent to $b$^$2$$=r$. (BTW - I have a PhD in mathematics, not that it really matters in this case, because this is only high-school level stuff.) Kiwima (talk) 05:01, 22 February 2016 (UTC)

The fifth definition should be kept; before the 20th century, "index" and "exponent" were used interchangeably, each referring to both the power to which some expression was raised and the index of a root. It should probably be changed from "rare" to "obsolete", though. For example:

• 1845, Encyclopædia metropolitana: "The notation by which the root is expressed, is the mark ${\sqrt {}}$ called a radical, placed over the letter, with an exponent to the left indicating the order of the root."
• 1717, A Treatise of Algebra in Two Books: "the Exponent of the m-Root (or 1/m Power) is 1/m times the Exponent of the Root."
• 1711, M. Ozanam's Introduction to the mathematicks: or, his Algebra: "its Exponent may be commenſured by the Exponent of the Root; namely for the Square Root by 2, for the Cube by 3, &c."

Vorziblix (talk) 12:16, 6 March 2016 (UTC)

{{look}}

I feel like more expertise is needed for this one. bd2412 T 02:08, 10 August 2016 (UTC)

I would keep the root sense (the one labeled obsolete)—I'm unfamiliar with that usage and wouldn't use the word that way, so if the usage exists, I think we should document it. I'm not sure about the logarithm sense. Pinging User:Msh210 for another opinion. —Mr. Granger (talk • contribs) 18:27, 12 August 2016 (UTC)

Thanks for the ping. The radical index sense seems cited by Vorziblix. The other ("The result of a logarithm") I'm unfamiliar with, personally, but that doesn't mean much. This is an RFV issue, no? Why is it here?​—msh210℠ (talk) 15:37, 15 August 2016 (UTC)

Partly cited: the "degree to which the root of a radicand is found" sense is now cited; still waiting for consensus on the "result of a logarithm" sense. — SMUconlaw (talk) 19:37, 19 August 2016 (UTC)

┌────────────────────────────────────────────────────────────────────────────────────────────────────┘ I did a bit of rooting around, and agree with @Kiwima that the "logarithm" sense should be deleted. From what I gathered (see, for example, [1]), a logarithm is another way of expressing an exponent. Thus, if $y=b^{x}$, then $log_{b}y=x$. In other words, $x$, the exponent of $b$, can be expressed as a logarithm. However, the word exponent here is still being used in the sense of "The power to which a number, symbol or expression is to be raised", and not some distinct sense. — SMUconlaw (talk) 14:59, 21 August 2016 (UTC)

Your argument seems to boil down to "exponent refers to a number independent of where in an expression it appears". By that logic, the radical-index sense should also be removed (and the sense we retain should be rewritten). In contrast, our current trifurcation of senses assumes exponent refers to a number as included in an expression. You may be absolutely correct. I don't know how we'd test whether you are.​—msh210℠ (talk) 17:00, 22 August 2016 (UTC)

I only studied mathematics up to Year 12 so I'm no expert, but sense 2 and sense 4 seem to use the word exponent differently. It's not just that exponent means "a number independent of where in an expression it appears". Sense 2 defines it as "The power to which a number, symbol or expression is to be raised"; the exponent $2$ in the expression $10^{2}$ indicates that $10$ is being raised to the second power, i.e., $10\times 10$. I assume this is the sense familiar to all of us. On the other hand, sense 4 seems to use the word to mean the nth root of a number; the exponent $3$ in the expression ${\sqrt[{3}]{2}}7$ indicates the cube root of $27$. On the other hand, sense 2 is merely using exponent in the same way as sense 1. — SMUconlaw (talk) 17:57, 22 August 2016 (UTC)

If two senses are the same, they all are: In ${\sqrt[{3}]{8}}$, 3 is the exponent of 2.​—msh210℠ (talk) 19:07, 23 August 2016 (UTC)

But the sense 4 quotations seem to use the word slightly differently. To take your example, 3 is the exponent of the root of 8 which is being calculated. ${\sqrt[{3}]{8}}=2^{3}$, but in the latter case (sense 2) the exponent, 3, is the power to which 2 is raised. On the other hand, if you have a look at works talking about exponents in the context of logarithms, they just seem to be referring to sense 2. I should add, though, that the OED only states sense 2. — SMUconlaw (talk) 19:40, 23 August 2016 (UTC)

Can we resolve this by indenting sense 3 to present it as a subsense or specialized sens of sense 2? At this point, I am not seeing a consensus to delete anything, although we may need an editorial discussion to make sure that our definitions are as clear and precise as possible. bd2412 T 19:05, 28 August 2016 (UTC)

I guess that's fine. Or do you think we should try leaving a message at "w:Wikipedia talk:WikiProject Mathematics" to see if a subject-area expert can help? — SMUconlaw (talk) 07:37, 30 August 2016 (UTC)

I have asked. Cheers! bd2412 T 14:41, 2 September 2016 (UTC)

Thanks. Let's hope we get some useful responses. — SMUconlaw (talk) 16:30, 2 September 2016 (UTC)

The consensus there appears to be that all three mathematical senses should be included. bd2412 T 22:51, 3 September 2016 (UTC)

• I think defining "exponent" as the argument of an inverse logarithm (sense 3) is self-explanatory from the definitions of logarithm and antilogarithm, and should probably be removed as redundant. The wording used is confusing in the definition, and seems to be a conflation between exponents (powers) and the results of exponentiation (unless it is an outdated sense). Essentially an exponentiation is the same function as an antilogarithm (an inverse logarithm), so that f(a, b) = a^b = antilog_a(b) = log_a⁻¹(b) = H₃(a, b), with exponentiation, antilogarithm, inverse logarithm, third hyperoperation, and iterative multiplication all being synonymous terms. If anything, I would suggest just changing it to "(rare) The result of an antilogarithm or exponentiation." Nicole Sharp (talk) 23:31, 3 September 2016 (UTC)
• Sense 4 is also redundant and self-explanatory from the definitions of powers and roots. Roots are by definition a form of exponentiation, where ^b√(a) = a^1/b = antilog_1/b(a), so that the n-th root of x is also the reciprocal-n-th exponent (power) of x. Nicole Sharp (talk) 23:50, 3 September 2016 (UTC)
• In sum, exponents, antilogarithm arguments, and roots are all mathematically equivalent. I would say the only advantage of keeping them as separate definitions of "exponent" is for users who are unaware of the different mathematical forms of exponentiation and may not realize that they are different expressions of the same thing. Nicole Sharp (talk) 23:57, 3 September 2016 (UTC)
  • That was the feeling behind my earlier suggestion to indent them a notch and keep them (or at least one of them) as subsenses. I think we rarely use subsenses, but they are useful where appropriate. bd2412 T 01:26, 4 September 2016 (UTC)
  • That is an excellent idea. Keep just the one mathematical sense, and then list how that sense is used within different contexts (e.g. roots, antilogarithms, etc.) as subsenses. I see that the math PhD above also agrees to remove the redundant senses. I'm Kappa Mu Epsilon myself. Nicole Sharp (talk) 01:41, 4 September 2016 (UTC)

Resolved by converting the contested senses into subsenses. bd2412 T 19:47, 4 September 2016 (UTC)

As a late comment, I support the use of subsenses. - -sche (discuss) 01:54, 7 September 2016 (UTC)

Evidence for existence of /ˈɛkspənənt/ pronunciation

https://www.youtube.com/watch?v=tRNTiEuXaMs Just after 2:45 for example

MimiKal797 (talk) 09:51, 11 March 2022 (UTC)