<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">I am happy with this. I just wanted to remind everybody that the nonstandard system allows really simple, intuitive proofs.<br><div> <span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 11px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div>Larry</div></div></span> </div><br><div><div>On 2 Jul 2008, at 17:45, Brian Huffman wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: -webkit-monospace; font-size: 10px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; ">Here's how I see it: If all you want to do is *use* analysis (e.g. maybe you just want to calculate derivatives) then you won't notice any difference between NSA and standard analysis. The same theorems have been proved in either version. I expect that the users who benefit most from having the real number theories in HOL would generally fall into this camp.<br><br>On the other hand, if you want to *prove* things *in* analysis, then the difference between standard and non-standard is immediately apparent.<br><br>I wouldn't consider NSA to be "buried" - until very recently, the NSA theories were located in a logic image separate from the main HOL image. If we split NSA as I have proposed, then it will be in a logic image separate from HOL, just as it was before.<br></span></blockquote></div><br></body></html>