The theoretical maximum for the PS3 shipment is 90.2M (as of Dec 2014). This is true if you believe the PS2 shipped 0 units during FY12 (Apr 12 - Mar 13 total of 16.5M). Likewise, the theoretical minimum for the PS3 is 73.7M as of December 2014. This is true if you believe the PS2 shipped 16.5M during FY12.

For fun, the theoretical maximum for the 360 shipment is 95.4M (as of Mar 2015). This is true if you believe the Xbone shipped 0 units during FY14 Q4 and FY15 (total 11.7M). Likewise, the theoretical minimum for the 360 is 83.7M as of March 2015. This is true if you believe the Xbone shipped 11.7M during that time period.

The reason I post these numbers is so that people know what they are working with when estimating something. It's unlikely either one of these systems will reach 100M. I had predicted the PS3 would, but I also expected the price of the machine to be $149 right now, at the most, with a price drop to $129 next year and $99 the year after. I can't believe how expensive these systems still are.

We don't know when the wii will peak nor how much it will sell on it's peak year. fact remains that your original claim is wrong. wii u sales are independant of the declining ps3 sales. One can predict wii u will sell any number while thinking ps3 won't cross 90m.

Sure I can make the claim the Wii U will sell 6 billion. Doesn't make it a  rational nor logical prediction. We can make decent assumptions based on historical data. 

Historical data says wii u still has some years left with good support and hasn't gotten a good price cut yet. Meanwhile, ps3 is almost 9 years old and continuously declining. with the current sales, it's an impossibility for ps3 to reach wii numbers, but wii u can still reach and exceed your example.

Yet it also says that Nintendo consoles tend to peak around their second (Gamecube) or third year (most of their other consoles.) With a Nintendo home console likely releasing in late 2017 it is unlikely that the Wii U will have longevity to make up for its very likely decline in sales. If it maintained the sales of this year (which will probably be something like 4.5 million at most - it will take three and a half years to reach its goal.) That is IF it maintained 2015 sales and 2015 sales are at their upper-end. 

The PS3 will not catch the Wii and I've been saying so for a long time, it would need steady sales in the same region as last year for another five years or so; that's almost PS2 level of lifecycle and just isn't happening.
The Wii U will not sell 25 million either, it's just moving too slowly and has been from the beginning, it is also likely facing a rather early replacement and certainly before the other two.

The PS3 will end up somewhere north of 90 million, I think 93-94 million would be the best possible outcome. As for the Wii U; I said about 1.5 year ago that it would sell in the region of 18-25 million and this is holding true but the upper part of that number is not achieveable any longer, it has sold less than 40% of that in over 2.5 years, I think 18 million is a better target now, it could end up under that if it is relieved next holiday (which I personally believe it will be).

Time will tell, but I am 100% certain that neither will reach those figures in the OP.

If you underestimate wii u, sure. remember it still didn't get a proper price cut. It can sell much more than 4.5m a year.

The gamecube had a many price-cuts, and very fast. The console was at $99 half way in its life. It didn't help the Gamecube. I expect the Wii U to be anywhere between 18 - 22 million. 

At one point, I believed it was possible for PS3 to, not necessarily beat the Wii, but to at least pass 100 million units. I guess I can see it happening, but PS3 would have to maintain that 3.6 million-ish per year, for at least 4 more years, for even that to happen, and I don't think it can do that. PS2 had that continuing momentum because of PS3's rocky start. PS4 has been fortunate enough to have an amazing start, and that's only gonna make the PS3's chances even slimmer.

For Wii-U, unless it starts tracking above GC numbers, I can't see it selling more than 20 million lifetime, and that would be pushing it, given the announcement of NX and even Nintendo seemingly slowly giving up.

"and that would be pushing it, given the announcement of NX and even Nintendo seemingly slowly giving up."

NX wasn't announced, it's probably a handheld and please show me evidence of nintendo "slowly giving up".