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This thing was a fucking pain in the ass to compile. Namely due to all the different quotes, et cetera, but it's finally finished! Enjoy!
Goku, Innocent Boo, Goku & Vegeta
Gotenks Pre-RoSaT
Super Boo & Gotenks Post and Ultimate Gohan
Buff Boo, Kid Boo & Goku Ssj3
Arguments & Counter Arguments
Gotenks SSj Pre
Gotenks SSj3 Post
:what
Goku, Innocent Boo, Goku & Vegeta
Fat Boo > Goku Ssj3 > Goku Ssj2 =/= Vegeta Ssj2
Supporting Evidence:
Supporting Evidence:
Gotenks {Predicted} > Innocent Boo > Goku Ssj3 > Goku Ssj2 =/= Majin Vegeta Ssj2
Supporting Evidence:
{Gotenks Predicted} > Innocent Boo > Goku SSj3 > Gotenks Base Pre
Support Evidence:
{Gotenks Predicted} > Innocent Boo > Gotenks Ssj Pre > Gotenks Base Pre
Supporting Evidence:
Gotenks makes the mistake of believing that his strength increased in proportion to his speed. Speed does not correlate with strength: http://dbzeta.net/viewtopic.php?t=3609
The two attributes are related, but they do not scale linearly. Because Gotenks probably wasn’t sensed from the Kaioshin realm and nobody notices his Ki from there, than he’s even weaker than Goku SSj3 and he didn’t live up to the prediction.
Supporting Evidence:
Gotenks Pre RoSaT was predicted to be stronger than both Goku and Innocent Boo. However, no Chi sensors confirm this prediction. Also, two of these statements were based on a false pretence before Goku had the opportunity to witness the full power of Goten and Trunks. After witnessing their full Chi gathered to their limits, he changes his opinion from ‘if they just manage to perform successfully’ to ‘If they master’ fusion.
{Gotenks Predicted} > Innocent Boo > Goku SSj3 > Gotenks Base Pre
Support Evidence:
{Gotenks Predicted} > Innocent Boo > Gotenks Ssj Pre > Gotenks Base Pre
Supporting Evidence:
Gotenks makes the mistake of believing that his strength increased in proportion to his speed. Speed does not correlate with strength: http://dbzeta.net/viewtopic.php?t=3609
The two attributes are related, but they do not scale linearly. Because Gotenks probably wasn’t sensed from the Kaioshin realm and nobody notices his Ki from there, than he’s even weaker than Goku SSj3 and he didn’t live up to the prediction.
Gotenks {Predicted} > Super Boo (Initial) =/= Innocent Boo > Gotenks Ssj Pre > Gotenks Base Pre
Supporting Evidence:
Super Boo (Power-Burst) > Gotenks {Predicted} > Super Boo (Initial) =/= Innocent Boo > Gotenks Ssj Pre > Gotenks Base Pre
Supporting Evidence:
http://z.mfcdn.net/store/manga/214/40-291.0/compressed/ddragon_ball_z_v024-181.jpg
http://z.mfcdn.net/store/manga/214/41-292.0/compressed/ldragon_ball_z_v025-010.jpg
http://z.mfcdn.net/store/manga/214/41-292.0/compressed/ldragon_ball_z_v025-019.jpg
Other notable Ki sensors don’t notice Boo’s power-up, only those that were paying close attention. Piccolo tells Kuririn that Boo has powered up and Kuririn has hopes based on Goku’s prediction, not that Gotenks Ssj actually lived up to the prediction when he became a Super Saiyan.
This also means Boo's power-up was a power-burst. This is further proven as Boo continues to examine himself after his power burst and the fact that Goten & Trunks think that only his appearance has changed.
Super Boo’s actual energy reading exceeds what he’s currently displaying, which they believe is the same as he was before.
Super Boo (Power-Burst/Full Power) > Gotenks {Predicted} > Super Boo (Initial) =/= Innocent Boo >= Gotenks Ssj Post > Gotenks Base Post > Gotenks Ssj Pre
Supporting Evidence:
Trunks makes a battle power related statement about Gotenks Base being able to take down Boo. So they go along with his plan and it’s immediately contradicted. This is still following the belief that 'Super Boo (Initial) =/= Innocent Boo'
Gotenks SSj3 Post =/= Super Boo > Gotenks {Predicted} > Super Boo (Initial) =/= Innocent Boo >= Gotenks Ssj Post > Gotenks Base Post > Gotenks Ssj Pre
Supporting Evidence:
Super Boo (Full Power) =/= Super Boo (Power-Burst) > Gotenks Ssj3 Post > Gotenks {Predicted} > Super Boo (Initial) =/= Innocent Boo >= Gotenks Ssj Post > Gotenks Base Post > Gotenks Ssj Pre
Ultimate Gohan > Super Boo =/= Gotenks SSj3 Post > Gotenks {Predicted} > Super Boo (Initial) =/= Innocent Boo >= Gotenks Ssj Post > Gotenks Base Post > Gotenks Ssj Pre
Supporting Evidence:
Supporting Evidence:
The product of the sum split, and rearranged who was in charge of body and power. Nothing more... yet.
Super Boo (Power-Burst) > Gotenks {Predicted} > Super Boo (Initial) =/= Innocent Boo > Gotenks Ssj Pre > Gotenks Base Pre
Supporting Evidence:
http://z.mfcdn.net/store/manga/214/40-291.0/compressed/ddragon_ball_z_v024-181.jpg
http://z.mfcdn.net/store/manga/214/41-292.0/compressed/ldragon_ball_z_v025-010.jpg
http://z.mfcdn.net/store/manga/214/41-292.0/compressed/ldragon_ball_z_v025-019.jpg
Other notable Ki sensors don’t notice Boo’s power-up, only those that were paying close attention. Piccolo tells Kuririn that Boo has powered up and Kuririn has hopes based on Goku’s prediction, not that Gotenks Ssj actually lived up to the prediction when he became a Super Saiyan.
This also means Boo's power-up was a power-burst. This is further proven as Boo continues to examine himself after his power burst and the fact that Goten & Trunks think that only his appearance has changed.
Super Boo’s actual energy reading exceeds what he’s currently displaying, which they believe is the same as he was before.
Super Boo (Power-Burst/Full Power) > Gotenks {Predicted} > Super Boo (Initial) =/= Innocent Boo >= Gotenks Ssj Post > Gotenks Base Post > Gotenks Ssj Pre
Supporting Evidence:
Trunks makes a battle power related statement about Gotenks Base being able to take down Boo. So they go along with his plan and it’s immediately contradicted. This is still following the belief that 'Super Boo (Initial) =/= Innocent Boo'
After becoming a Super Saiyan, the battle is much closer and Boo is unable to maintain complete control of the fight. He’s still fighting at Innocent Boo’s level and Gotenks has finally near his expected battle power.
Gotenks SSj3 Post =/= Super Boo > Gotenks {Predicted} > Super Boo (Initial) =/= Innocent Boo >= Gotenks Ssj Post > Gotenks Base Post > Gotenks Ssj Pre
Supporting Evidence:
After becoming a Super Saiyan 3 the battle appears to be significantly closer.
Super Boo (Full Power) =/= Super Boo (Power-Burst) > Gotenks Ssj3 Post > Gotenks {Predicted} > Super Boo (Initial) =/= Innocent Boo >= Gotenks Ssj Post > Gotenks Base Post > Gotenks Ssj Pre
Ultimate Gohan > Super Boo =/= Gotenks SSj3 Post > Gotenks {Predicted} > Super Boo (Initial) =/= Innocent Boo >= Gotenks Ssj Post > Gotenks Base Post > Gotenks Ssj Pre
Supporting Evidence:
Buff Boo > Super Boo =/= Gotenks Ssj3 Post
When Super Boo transformed into Buff Boo his Ki was noted as increasing, but it was never noted as decreasing. Because no such evidence exists, the simple answer is that it did not decrease.
Kid Boo > Buff Boo > Gotenks Ssj3 Post =/= Super Boo
Supporting Evidence:
This particular statement is ambiguous, so my interpretation is as valid as your own. Both absorptions weakened Boo.
Ultimate Gohan > Goku SSj3 > Kid Boo > Buff Boo > Gotenks Ssj3 Post =/= Super Boo (Power-Burst) > Gotenks {Predicted} > Super Boo (Initial) =/= Innocent Boo >= Gotenks SSj Post > Gotenks Base Post > Gotenks Ssj Pre > Gotenks Base P
Supporting Evidence:
So Goku’s prediction about Gotenks and Boo was based on a false pretence the entire time.
When Super Boo transformed into Buff Boo his Ki was noted as increasing, but it was never noted as decreasing. Because no such evidence exists, the simple answer is that it did not decrease.
Kid Boo > Buff Boo > Gotenks Ssj3 Post =/= Super Boo
Supporting Evidence:
This particular statement is ambiguous, so my interpretation is as valid as your own. Both absorptions weakened Boo.
Ultimate Gohan > Goku SSj3 > Kid Boo > Buff Boo > Gotenks Ssj3 Post =/= Super Boo (Power-Burst) > Gotenks {Predicted} > Super Boo (Initial) =/= Innocent Boo >= Gotenks SSj Post > Gotenks Base Post > Gotenks Ssj Pre > Gotenks Base P
Supporting Evidence:
So Goku’s prediction about Gotenks and Boo was based on a false pretence the entire time.
Arguments & Counter Arguments
Gotenks SSj Pre
Argument
a) Gotenks Base Pre-RoSaT survived Majin Boo, Vegeta didn't; therefore he has to be around Super Saiyan 2 power.
Counter-Argument
There are countless scenarios where a weaker fighter survives a stronger fighter, but it doesn't mean they are stronger than anybody else. Some examples include Hercule fighting Perfect Cell & Kid Boo. Vegeta in his Ssj2 & Base form being mercilessly assaulted by Kid Boo -who is not known to hold back power. Kaioshin surviving Boo. Surviving a fight doesn't account for anything.
Argument
b) Gotenks says Gotenks' will defeat Majin Boo and it isn't contradicted.
Counter-Argument
Goku made the statement prior to being able to accurately gauge the strength of the boys. Therefore it's not an accurate power statement and is contradicted when he isn't even certain if what they're showing them is their full power.
Argument
c) Goku didn't think they needed the RoSaT
Counter-Argument
Actually, within the context of the statement Goku only says 'no' to using it for the sole purpose of speeding up the time it will take to learn the fusion. He later says 'they might need it later'. This also contradicts the notion that Gotenks' strength wasn't contradicted and debunks the notion that he didn't intend for them to use the RoSaT.
Argument
d) Goku isn't an idiot, he wouldn't risk the entire Universe unless he was certain the boys could win.
Counter-Argument
Gotenks was remarked as being able to win 'one way or another', this doesn't have to include battle power as Goku has seen the fusion before and knows it likely yields some weird powers.
Additionally, Piccolo says the same thing to Gotenks about both Boo's: that he needs to 'train and train' in preparation for both fights. The statement isn't contradicted in either situation, therefore it's true until contradicted.
Also, Goku figured they would learn to fuse quickly, which would give them the remainder of the time to focus on training, and if need be, they could use the RoSaT. So no, Goku isn't an idiot, but it doesn't mean Gotenks Ssj Pre-RoSaT would be strong enough to defeat Majin Boo without the benefits of training, because Goku wasn't certain if he would be or not.
Argument
e) Piccolo only question Gotenks' speed, not his power.
Counter-Argument
My analysis in another topic proves that speed doesn't correlate with strength in linear progression. Hence why Piccolo was testing him. Gotenks was foolish enough to believe so, but this is completely false. Ginyu was 33% stronger than Goku on Namek, but he was much slower. Because speed & strength can differ so greatly from one another, it makes it impossible to judge a characters power based solely on speed alone.
Argument
f) Goku says Gotenks will be stronger than him and it isn't contradicted.
Counter-Argument
Note: Goku actually never told Boo this (apparently he's gone senile in the afterlife).
Argument:
g) Goku is stupid and a serial killer because he let 10% of the Earth die.
Counter-Argument:
Piccolo was willing to let Super Boo annihilate the entire population (7 Billion people, or the remaining 90%) for the sole purpose of giving Gotenks a chance to close the gap.
Goku knows they still have the Dragon Balls and previously told Gohan during the Cell Games not to worry about whatever damage he does because it can all be reversed with the Dragon Balls.
After Kid Boo appeared, Goku was teleported to the World Of The Kais and he says:
Goku: “It’s alright. I’m tellin’ ya, don’t worry. He can’t come all the way here. We’ll think up some sorta strategy. I feel bad for the aliens who will be sacrificed in the meantime, but we’ll use the dragonballs later…”
Goku is willing to make the sacrifice to give Gotenks a chance to succeed, because all the damage can later be undone.
Argument:
Goku didn't intend for them to use the RoSaT.
Counter-Argument:
Actually, if you look at the context of the statement:
So finally, Goku isn't 100% certain if Gotenks, even as a Super Saiyan, would become strong enough. The RoSaT was a back-up plan just in case he wasn't. This also debunks pretty much all the Gotenks Pre-RoSaT arguments.
Argument
a) Fusion doesn't scale linearly.
Counter-Argument
This particular argument uses the quote from Piccolo that says 'even if you get just a little stronger, it will be more effective when you perform fusion'. All this means is 'Goten + 1 / Trunks + 1 = Gotenks +n 2'.
Therefore 'Gotenks Base Post > Gotenks Ssj Pre' is hereby disproven. Additionally, Piccolo started to build hope based off how perfectly the boys performed the fusion dance and built his expectations off of a 'not fully powered' Gotenks.
Fusion does scale linearly. There is no evidence to suggest it doesn't. This argument is a desperate cop-out to make the 'Base Post > Ssj Pre' theory work. It's both a numeric impossibility and a logical fallacy due to having no evidence to substantiate the claim.
P.S.
For the people who actually believe that fusion doesn't scale linearly, than you are creating a paradox and a big hole in your logic by believing Goku can sense the Metamoran individuals and their fused product and determine what Gotenks Ssj Pre will be.
Your logic collapses in on itself.
Argument:
Piccolo didn't doubt Gotenks' when he said he could finish Boo.
Counter-Argument:
Piccolo didn't have the time to contradict Gotenks' whom flew off almost immediately. Piccolo resorts to trying to stop him because of the amount of time they have left and they would ultimately defuse and then Earth's only hope would be killed off. However, don't make the mistake of thinking that's the same as Piccolo not doubting their strength. He never had the time to vocalize his doubts and even with what he was able to say to himself, the safety of the individuals was clearly more paramount.
Argument: Piccolo let them sleep after seeing Gotenks Super Saiyan, this means he thinks the fusion is strong enough.
Counter-Argument: Piccolo let the boys sleep prior to even merging successfully for the first time, and they only had 1 day left to learn the fusion. This argument is bullshit.
Argument: How can Gotenks be weaker than Boo as a Super Saiyan?
Counter-Argument: After Kibito & Kaioshin merged with the Potara, their strength wasn't even considered on par with Vegeta Ssj2; yet Kaioshin alone was considered a dimension above Piccolo, and because the Potara has greater affect than the Metamoran fusion, this makes it a mathematical impossibility for Gotenks Ssj Pre-RoSaT to actually surpass Fat Boo.
a) Gotenks Base Pre-RoSaT survived Majin Boo, Vegeta didn't; therefore he has to be around Super Saiyan 2 power.
Counter-Argument
There are countless scenarios where a weaker fighter survives a stronger fighter, but it doesn't mean they are stronger than anybody else. Some examples include Hercule fighting Perfect Cell & Kid Boo. Vegeta in his Ssj2 & Base form being mercilessly assaulted by Kid Boo -who is not known to hold back power. Kaioshin surviving Boo. Surviving a fight doesn't account for anything.
Argument
b) Gotenks says Gotenks' will defeat Majin Boo and it isn't contradicted.
Counter-Argument
Goku made the statement prior to being able to accurately gauge the strength of the boys. Therefore it's not an accurate power statement and is contradicted when he isn't even certain if what they're showing them is their full power.
Argument
c) Goku didn't think they needed the RoSaT
Counter-Argument
Actually, within the context of the statement Goku only says 'no' to using it for the sole purpose of speeding up the time it will take to learn the fusion. He later says 'they might need it later'. This also contradicts the notion that Gotenks' strength wasn't contradicted and debunks the notion that he didn't intend for them to use the RoSaT.
Argument
d) Goku isn't an idiot, he wouldn't risk the entire Universe unless he was certain the boys could win.
Counter-Argument
Gotenks was remarked as being able to win 'one way or another', this doesn't have to include battle power as Goku has seen the fusion before and knows it likely yields some weird powers.
Additionally, Piccolo says the same thing to Gotenks about both Boo's: that he needs to 'train and train' in preparation for both fights. The statement isn't contradicted in either situation, therefore it's true until contradicted.
Also, Goku figured they would learn to fuse quickly, which would give them the remainder of the time to focus on training, and if need be, they could use the RoSaT. So no, Goku isn't an idiot, but it doesn't mean Gotenks Ssj Pre-RoSaT would be strong enough to defeat Majin Boo without the benefits of training, because Goku wasn't certain if he would be or not.
Argument
e) Piccolo only question Gotenks' speed, not his power.
Counter-Argument
My analysis in another topic proves that speed doesn't correlate with strength in linear progression. Hence why Piccolo was testing him. Gotenks was foolish enough to believe so, but this is completely false. Ginyu was 33% stronger than Goku on Namek, but he was much slower. Because speed & strength can differ so greatly from one another, it makes it impossible to judge a characters power based solely on speed alone.
Argument
f) Goku says Gotenks will be stronger than him and it isn't contradicted.
Counter-Argument
The entire point of telling Majin Boo that was buy time for the boys to learn the fusion. It wasn't meant to be taken as an actual fact. Then there is this:
Note: Goku actually never told Boo this (apparently he's gone senile in the afterlife).
Argument:
g) Goku is stupid and a serial killer because he let 10% of the Earth die.
Counter-Argument:
Piccolo was willing to let Super Boo annihilate the entire population (7 Billion people, or the remaining 90%) for the sole purpose of giving Gotenks a chance to close the gap.
Goku knows they still have the Dragon Balls and previously told Gohan during the Cell Games not to worry about whatever damage he does because it can all be reversed with the Dragon Balls.
After Kid Boo appeared, Goku was teleported to the World Of The Kais and he says:
Goku: “It’s alright. I’m tellin’ ya, don’t worry. He can’t come all the way here. We’ll think up some sorta strategy. I feel bad for the aliens who will be sacrificed in the meantime, but we’ll use the dragonballs later…”
Goku is willing to make the sacrifice to give Gotenks a chance to succeed, because all the damage can later be undone.
Argument:
Goku didn't intend for them to use the RoSaT.
Counter-Argument:
Actually, if you look at the context of the statement:
Goku wasn't saying that the boys didn't need the RoSaT because the fusion on it's own would be strong enough to defeat Boo, he was neglecting in using it as a means for the boys to learn the Metamoran quicker, which would waste time. He than blatantly says 'They might NEED IT LATER' because they are going to learn to fuse quickly.
So finally, Goku isn't 100% certain if Gotenks, even as a Super Saiyan, would become strong enough. The RoSaT was a back-up plan just in case he wasn't. This also debunks pretty much all the Gotenks Pre-RoSaT arguments.
Argument
a) Fusion doesn't scale linearly.
Counter-Argument
This particular argument uses the quote from Piccolo that says 'even if you get just a little stronger, it will be more effective when you perform fusion'. All this means is 'Goten + 1 / Trunks + 1 = Gotenks +n 2'.
Therefore 'Gotenks Base Post > Gotenks Ssj Pre' is hereby disproven. Additionally, Piccolo started to build hope based off how perfectly the boys performed the fusion dance and built his expectations off of a 'not fully powered' Gotenks.
Fusion does scale linearly. There is no evidence to suggest it doesn't. This argument is a desperate cop-out to make the 'Base Post > Ssj Pre' theory work. It's both a numeric impossibility and a logical fallacy due to having no evidence to substantiate the claim.
P.S.
For the people who actually believe that fusion doesn't scale linearly, than you are creating a paradox and a big hole in your logic by believing Goku can sense the Metamoran individuals and their fused product and determine what Gotenks Ssj Pre will be.
Your logic collapses in on itself.
Argument:
Piccolo didn't doubt Gotenks' when he said he could finish Boo.
Counter-Argument:
Piccolo didn't have the time to contradict Gotenks' whom flew off almost immediately. Piccolo resorts to trying to stop him because of the amount of time they have left and they would ultimately defuse and then Earth's only hope would be killed off. However, don't make the mistake of thinking that's the same as Piccolo not doubting their strength. He never had the time to vocalize his doubts and even with what he was able to say to himself, the safety of the individuals was clearly more paramount.
Argument: Piccolo let them sleep after seeing Gotenks Super Saiyan, this means he thinks the fusion is strong enough.
Counter-Argument: Piccolo let the boys sleep prior to even merging successfully for the first time, and they only had 1 day left to learn the fusion. This argument is bullshit.
Argument: How can Gotenks be weaker than Boo as a Super Saiyan?
Counter-Argument: After Kibito & Kaioshin merged with the Potara, their strength wasn't even considered on par with Vegeta Ssj2; yet Kaioshin alone was considered a dimension above Piccolo, and because the Potara has greater affect than the Metamoran fusion, this makes it a mathematical impossibility for Gotenks Ssj Pre-RoSaT to actually surpass Fat Boo.
Gotenks SSj3 Post
Argument: Gotenks Base Post-RoSaT surpassed his previous SSj level
Counter Argument: Actually no. For Goku to make any sort of estimate about the kids Pre-RoSaT, Fusion has to scale linearly or his argument is merely an opinion and not an actual fact. Additionally, for this argument to work, the boys would have to surpass their previous Super Saiyan level as well; this obviously did not happen.
Argument: Piccolo hoped for a miracle and Gotenks didn't let up.
Counter Argument: Because Gotenks Base Post-RoSaT didn't surpass his previous power as a Super Saiyan (see point above), this also means that Piccolo was simply jumping to conclusions. If we pay attention to the artwork, Piccolo begins to celebrate at how well the boys performed the fusion dance, and he continues this train of thought until Gotenks actually fights; a result of which makes him immediately retract his previous statement, and Majin Boo is not shown to power up.
Argument: Piccolo doubted Gotenks Ssj Pre's Power but not Gotenks Base Post
Counter Argument: See the first two points above.
Argument: Piccolo said 'even Gotenks there couldn't beat you', this has to mean he's stronger than anybody who came before-hand.
Counter Argument: Incorrect. All this statement means is that Piccolo believes Gotenks is the last hope alive (Goku is gone, Vegeta is dead & Gohan is believed dead).
Argument: Gotenks is stronger than Super Boo
Counter-Argument: Super Boo remarks himself as the strongest prior to Gohan's arrival. He hears that Gotenks's fusion only lasts for so long. As soon as he senses Gohan's Chi he begins to orchestrate the plan to absorb Gotenks. Because Super Boo's statement comes 'after' the feats in their battle, than it contradicts what originally happened. Remember: Toriyama makes the story up as he goes along.
Argument: Gotenks has to have Super Saiyan 2.
Counter-Argument: Actually no. Goku already demonstrated Super Saiyan 1-3 against the Fat Majin Boo and Goten was watching this entire demonstration. Goten is also the one who says: 'I can't believe there is something beyond Super Saiyan', and Trunks doesn't contradict his statement. This means they went from Super Saiyan 1 right to Super Saiyan 3.
Argument: Gotenks had sparks in one panel, that means he was Super Saiyan 2!
Counter-Argument: Vegetto had sparks when he transformed into Super Saiyan. Nappa had sparks when he powered up. These 'sparks' can simply be the result of Gotenks transforming into Super Saiyan 3; which is essentially what he's doing.
Argument: Even if Gotenks doesn't have Super Saiyan 2 he still get's the boost.
Counter-Argument: The hell?
Counter Argument: Actually no. For Goku to make any sort of estimate about the kids Pre-RoSaT, Fusion has to scale linearly or his argument is merely an opinion and not an actual fact. Additionally, for this argument to work, the boys would have to surpass their previous Super Saiyan level as well; this obviously did not happen.
Argument: Piccolo hoped for a miracle and Gotenks didn't let up.
Counter Argument: Because Gotenks Base Post-RoSaT didn't surpass his previous power as a Super Saiyan (see point above), this also means that Piccolo was simply jumping to conclusions. If we pay attention to the artwork, Piccolo begins to celebrate at how well the boys performed the fusion dance, and he continues this train of thought until Gotenks actually fights; a result of which makes him immediately retract his previous statement, and Majin Boo is not shown to power up.
Argument: Piccolo doubted Gotenks Ssj Pre's Power but not Gotenks Base Post
Counter Argument: See the first two points above.
Argument: Piccolo said 'even Gotenks there couldn't beat you', this has to mean he's stronger than anybody who came before-hand.
Counter Argument: Incorrect. All this statement means is that Piccolo believes Gotenks is the last hope alive (Goku is gone, Vegeta is dead & Gohan is believed dead).
Argument: Gotenks is stronger than Super Boo
Counter-Argument: Super Boo remarks himself as the strongest prior to Gohan's arrival. He hears that Gotenks's fusion only lasts for so long. As soon as he senses Gohan's Chi he begins to orchestrate the plan to absorb Gotenks. Because Super Boo's statement comes 'after' the feats in their battle, than it contradicts what originally happened. Remember: Toriyama makes the story up as he goes along.
Argument: Gotenks has to have Super Saiyan 2.
Counter-Argument: Actually no. Goku already demonstrated Super Saiyan 1-3 against the Fat Majin Boo and Goten was watching this entire demonstration. Goten is also the one who says: 'I can't believe there is something beyond Super Saiyan', and Trunks doesn't contradict his statement. This means they went from Super Saiyan 1 right to Super Saiyan 3.
Argument: Gotenks had sparks in one panel, that means he was Super Saiyan 2!
Counter-Argument: Vegetto had sparks when he transformed into Super Saiyan. Nappa had sparks when he powered up. These 'sparks' can simply be the result of Gotenks transforming into Super Saiyan 3; which is essentially what he's doing.
Argument: Even if Gotenks doesn't have Super Saiyan 2 he still get's the boost.
Counter-Argument: The hell?
Toriyama states that both Super Saiyan 2 and Super Saiyan 3 derive from the original Super Saiyan transformation. This also means that SSj 3 doesn't derive from SSj2. Therefore you don't need it to acquire SSj3, you just need the base product, SSj. Think of it like building blocks. You start off with 1 block (SSj), and than you go to SSj2 and suddenly you have 2 blocks. Next you go to SSj3 and you have 8 blocks. Whereas if you jump from SSj to SSj3, you only wind up with 4 blocks. Same principal here.
