Your link seems to give quite a few similar definitions of what a public school is, but both colloquially and from a government perspective it seems to be that they should meet:
Non-local, fee-paying, expensive, endowed, boarding, selective and non-profit.
The side-effect of this is that they were traditionally reserved for the male children of elites. The boarding requirement seems to be weaker, as two day schools (St Paul’s and Merchant Taylor’s) are listed as part of the nine “major” public schools.
However, the working definition given in the Wikipedia article, and definition used by the British government for the Public Schools Commission means that there are almost 300 “public” schools in England and Wales
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Your list is supported as being part of the “major” public schools AKA Clarendon schools:
‘Today, while the hierarchical distinction is less commonly used, only the "Great Nine" public schools of England – Eton, Harrow, Winchester, Charterhouse, Merchant Taylors', Westminster, Shrewsbury, Rugby and St Paul's – are referred to as "major"[citation needed] on account of this historical association. Schools outside this group are referred to as "minor"[citation needed], irrespective of contemporary influence’
Citations are missing for that paragraph however, all throughout the article it’s made clear there are certainly a few hundred public schools, and not just a handful.
For instance, the link to the HMC page, of which membership seems to be more or less a good rule of them for a school being “public” : https://en.m.wikipedia.org/wiki/Headmasters%27_and_Headmistr...
Colloquially I do know that boys who attended Eton only acknowledge 3 or so other public schools, but the general public does have a broader definition. Nonetheless have a few hundred is still substantially less than the thousands which exist across England and Wales.
However, the working definition given in the Wikipedia article, and definition used by the British government for the Public Schools Commission means that there are almost 300 “public” schools in England and Wales .
Your list is supported as being part of the “major” public schools AKA Clarendon schools:
‘Today, while the hierarchical distinction is less commonly used, only the "Great Nine" public schools of England – Eton, Harrow, Winchester, Charterhouse, Merchant Taylors', Westminster, Shrewsbury, Rugby and St Paul's – are referred to as "major"[citation needed] on account of this historical association. Schools outside this group are referred to as "minor"[citation needed], irrespective of contemporary influence’
Citations are missing for that paragraph however, all throughout the article it’s made clear there are certainly a few hundred public schools, and not just a handful. For instance, the link to the HMC page, of which membership seems to be more or less a good rule of them for a school being “public” : https://en.m.wikipedia.org/wiki/Headmasters%27_and_Headmistr...
Colloquially I do know that boys who attended Eton only acknowledge 3 or so other public schools, but the general public does have a broader definition. Nonetheless have a few hundred is still substantially less than the thousands which exist across England and Wales.