గత టపాలో ప్రశ్న అర్ధరహితంగా ఉన్నదా? సరే ఇప్పుడు మరికొంచం వివరంగా.
ఇలా చూద్దాం
(*) a-b = a+b if b< b =" a+c">= 0; where c+b = 0 (pls. see foot note)
(#) a+b = a+b for all a and b.
(@) a+(-b) = a+c where c+b = 0.
*,#,@ మూడూ ఒకటేనా?
ఖచ్చితంగా *,# ఒకటే కాదు ఎందుకంటే
a+(b+c) = (a+b)+c for all a,b,c
a-(b-c) != (a-b)-c
మరి *,@ ఒకటే కాకపొతే వాటి మధ్య ఇలాంటి వైరుధ్యం ఏమైనా దొరుకుతుందా?
ఉత్తినే సరదాగా
---
a-b = a+b; as if now this is contradictory might confuse with a-b = a+|b| if b is negative, but my problem here is I am dealing things in Euclidean way, so these are the confusions faced by Early Mathematicians while dealing with definitions.
Anyway, as if now, the problem here is defining subtraction which is equivalent to addition, as both generate the same in R (real numbers).
Consider scenario, when only Natural numbers were known, so, a-b might be or might not be a Natural number, but what we know at present is in a-b, we need to add both if b is not a positive integer.
14 comments:
a-b = a+b if b< b ???
భా.రా.రే.గారు
జస్ట్ ఇప్పుడే ఎడిట్ చేశాను, అది అలా మారిపోయింది...
ఇప్పుడు సరిచేశాను.
Tara gaaru, you can delete my previous comment, but this is also valid
a-b = a+b if b<= 0
భా.రా.రే.గారు
తార గారు ఏంటి సార్ కొత్తగా..అస్సలు బాలేదు
>>a-b = a+b if b<= 0
అవునండి, అటుది ఇటు ఐనా, ఇటుది అటు ఐనా ఒకటే కదా మన పేస్టింగ్ లెమ్మా ప్రకారం, అందుకని అది వదిలేశాను.
a-b = a+b ONLY IF b = 0
not b<=0
a-b = a+b for all values of -|b|
My above comment is only valid in this particular scenario as a whole
a-b = a+b if b< 0
a-b = a+c if b>= 0; where c+b = 0
(*) a-b = a+b if b< 0 ??? how is this possible?
a-b = a+|b| if b< 0 is that what you meant ?
@Manchu, AFAIU from his previous post he is considering absolute values, but I am not clear what tara is trying to achieve here.
@manchu
>>a-b = a+b if b< 0 ??? how is this possible?
Yup, a-b= a+|b| if b<0, is valid, but my problem is I yet to define sign here, anyway, I will edit that to clear confusions.
@భా.రా.రే.గారు,
>>but I am not clear what tara is trying to achieve here.
Well, trying some thing new, first of all I want to show -,+ generate same set, but they are not one and the same.
Might be, this is not right way to start with, since with out info on "generate", but trying to catch bloggers pulse.
Tara,
are trying to get your home-work solved by these readers, here? No.. No.. that's not correct. :))
(*) a-b = a+b if b< b =" a+c">= 0; where c+b = 0
asalu naakemi arsham kaledu. konni kaarnaalu:
1. programming cheyatam valana "=" assignment laaga tostundi. cant help it :-(
2. if b< b =" a+c">= 0;
anaga emi? b < (b=a+c) anaa?
sodaharanamuga cheppandi (foot notes choodamani cheppoddu)
Seems there its another bug in Blogger, I edited that line thrice, and once more it showing some thing else.
a-b = a+b for all values of -|b|
Post a Comment